Resources

Resources

Write two-variable inequalities: word problems

April was asked to determine whether

f(x)=x^3-1

is even, odd, or neither. Here is her work:

\newline

1

: Find expression for

f(-x)

\newline

f(-x)=(-x)^3-1 =-x^3-1

\newline

2

f(-x)

f(x)

-f(x)

\newline

-x^3-1

-f(x)=-x^3-1

\newline

3

f(-x)

is equivalent to

-f(x)

f

\newline

Is April's work correct? If not, what is the first step where April made a mistake?

Layla is booking a band and a DJ for a dance, and wants to keep the cost of the entertainment under

\$650

. A band can play for part of the time at an hourly rate of

\$150

, and a DJ can play for the remaining time at an hourly rate of

\$65

. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x

= the number of hours the band will play

\newline

y

= the number of hours the DJ will play

Ezra is purchasing chocolate truffles to use as party favors. To ensure there are enough for everyone, he needs to purchase at least

228

pieces. Dark chocolate truffles come in boxes of

24

pieces and milk chocolate truffle comes in packs of

32

pieces. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x

= the number of boxes of dark chocolate truffles

\newline

y

= the number of boxes of milk chocolate truffles

A tour director is hiring boats to transport a group of tourists across a river. He must make sure there is room for at least

32

passengers, the number of tourists in the group. A dinghy can seat

5

passengers and a flatboat can seat

2

passengers. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x

= number of dinghies

\newline

y

= number of flatboats

Gina teaches arts and crafts to kids. She is handing out

p

popsicle sticks to each kid, and there are

5

kids in today's class. Gina will hand out

40

popsicle sticks in all.

\newline

Which diagram models the story?

\newline

\newline

Which equation models the story?

\newline

\newline

p/5 = 40

\newline

5p = 40

A company’s manager estimated that the cost

C

, in dollars, of producing

n

C = 7n + 350

. The company sells each item for

\$12

. The company makes a profit when the total income from selling a quantity of items is greater than the total cost of producing that quantity of items. Which of the following inequalities gives all possible values of

n

for which the manager estimates that the company will make a profit?

\newline

n < 70

\newline

n < 84

\newline

n > 70

\newline

n > 84

For all integers

x>0

f(x)

f(x)=\frac{f(x-1)}{(-1)^x}

f(1)=1

, which of the following statement is correct for the values of

f(x)

\newline

A) The values of

f(x)

for all even values of

x

\newline

B) The value of

f(x)

for all odd values of

x

\newline

C) The value of

f(x)

for all even values is

f(x)

0

and for all odd values is

f(x)

1

\newline

D) The value of

f(x)

f(x)

0

f(x)

1

Brenna is in the orchestra at her school. Both the orchestra and the band, along with any parents who want to go, are taking a field trip to a symphony. The orchestra purchases

24

student tickets and

8

adult tickets for

\$512

. The band purchases

30

student tickets and

15

adult tickets for

\$765

. This system of equations can be used to represent the situation:

\newline

24x + 8y = 512

\newline

30x + 15y = 765

\newline

Which statement is correct?

\newline

(A) In the system of equations,

x

represents the price of an adult ticket, and

y

represents the price of a student ticket.

\newline

(B) In the system of equations,

x

represents the total amount the band and orchestra spend on adult tickets, and

y

represents the total amount they spend on student tickets.

\newline

(C) In the system of equations,

x

represents the total amount the band and orchestra spend on student tickets, and

y

represents the total amount they spend on adult tickets.

\newline

(D) In the system of equations,

x

represents the price of a student ticket, and

y

represents the price of an adult ticket.

\newline

What is the total amount of money the band and orchestra spend on student tickets?

\newline

8

4

8

5

3x+y=1

\newline

y=

6x^{2}-4x-1

\newline

(x,y)

is a solution to the system of equations shown, which of the following are

\newline

x-coordinates of the solutions?

\newline

1

\newline

-\frac{1}{2}

\frac{5}{2}

\newline

-\frac{2}{3}

\frac{1}{2}

\newline

\frac{2}{3}

-\frac{1}{2}

\newline

\frac{2}{3}

-1

Alaina was asked whether the following equation is an identity:

\newline

(2 x+1)^{2}-(x+1)^{2}=3(x+1)^{2}-1

\newline

She performed the following steps:

\newline

(2 x+1)^{2}-(x+1)^{2}

\newline

\stackrel{\text { Step } 1}{\hookrightarrow}=4 x^{2}+4 x+1-x^{2}+2 x+1

\newline

\stackrel{\text { Step } 2}{\hookrightarrow}=3 x^{2}+6 x+2

\newline

\stackrel{\text { Step } 3}{\hookrightarrow}=3 x^{2}+6 x+3-1

\newline

\stackrel{\text { Step } 4}{\hookrightarrow}=3\left(x^{2}+2 x+1\right)-1

\newline

\stackrel{\text { Step } 5}{\hookrightarrow}=3(x+1)^{2}-1

\newline

For this reason, Alaina stated that the equation is a true identity.

\newline

Is Alaina correct? If not, in which step did she make a mistake?

\newline

1

\newline

(A) Alaina is correct.

\newline

(B) Alaina is incorrect. She made a mistake in step

1

\newline

(C) Alaina is incorrect. She made a mistake in step

3

\newline

(D) Alaina is incorrect. She made a mistake in step

5

A minor league hockey team has been collecting ticket sales data over the past year. At a current price of

\$ 25

per ticket, an average of

4000

seats are purchased. The team predicts that for each

\$ 1

increase in ticket price,

100

fewer tickets will be sold. Which of the following functions best models the amount of money that the hockey team expects to collect from ticket sales,

y

\$ x

increase in ticket price?

\newline

1

\newline

y=(25+x)(4000-100 x)

\newline

y=(25-x)(4000+100 x)

\newline

y=x(4000-100 x)

\newline

y=4000(25+x)

Johnny is building birdhouses in shop class, and he has a total of

349

nails on hand. A small birdhouse requires

20

nails and a large birdhouse requires

56

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of small birdhouses

\newline

y =

the number of large birdhouses

\newline

\newline

20 + x + 56 + y < 349

\newline

20x + 56y < 349

\newline

20 + x + 56 + y \leq 349

\newline

20x + 56y \leq 349

Roger is going to purchase some writing instruments at the school store, where mechanical pencils cost

\$2

\$1

. He can spend up to

\$8

, but not more.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of mechanical pencils Roger will buy

\newline

y =

the number of pens Roger will buy

\newline

\newline

\newline

2x + y \geq 8

\newline

2x + y \leq 8

\newline

x + 2y \leq 8

\newline

x + 2y \geq 8

Tommy is going to be participating in a long bike race soon. He needs to ride a total of at least

119

kilometers today. He plans to do this by riding multiple laps on the Highland Loop, which is

17

kilometers long, and the Pinehurst Loop, which is

49

kilometers long.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of laps on the Highland Loop

\newline

y =

the number of laps on the Pinehurst Loop

\newline

\newline

17x + 49y > 119

\newline

49x + 17y \geq 119

\newline

49x + 17y > 119

\newline

17x + 49y \geq 119

Alice, a purchasing agent for a high-tech firm, is ordering computers for a new branch office. Laptops cost

\$750

apiece and desktop computers cost

\$410

apiece. The budget for the computers is no more than

\$22,000

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of laptops ordered

\newline

y =

the number of desktop computers ordered

\newline

\newline

750x + 410y \geq 22,000

\newline

750x \times 410y \geq 22,000

\newline

750x \times 410y \leq 22,000

\newline

750x + 410y \leq 22,000

Linda is selling handmade jewelry to earn money for camp. Bracelets sell for

\$3

and necklaces sell for

\$15

, and she needs to make at least

\$320

in revenue to cover the cost of camp.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of bracelets

\newline

y =

the number of necklaces

\newline

\newline

3x + 15y \leq 320

\newline

3x + 15y > 320

\newline

3x + 15y \geq 320

\newline

3x + 15y < 320

Omar is buying soda and juice for a party and wants to spend no more than

\$45

\$2

per bottle, and juice costs

\$3

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of bottles of soda

\newline

y =

the number of bottles of juice

\newline

\newline

3x + 2y \leq 45

\newline

2x + 3y \leq 45

\newline

3x + 2y < 45

\newline

2x + 3y < 45

A tour director is hiring boats to transport a group of tourists across a river. He must make sure there is room for at least

27

passengers, the number of tourists in the group. A dinghy can seat

6

passengers and a flatboat can seat

1

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of dinghies

\newline

y =

the number of flatboats

\newline

\newline

6x + y \geq 27

\newline

x + 6y \geq 27

\newline

6x + y \leq 27

\newline

x + 6y \leq 27

Mrs. Fowler took her grandchildren to a baseball game, with plans to spend no more than

\$36

on snacks. An order of nachos costs

\$4

and a bag of peanuts costs

\$3

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of nacho orders

\newline

y =

the number of bags of peanuts

\newline

\newline

3x + 4y \leq 36

\newline

4x + 3y < 36

\newline

4x + 3y \leq 36

\newline

3x + 4y < 36

Jada is going to purchase some writing instruments at the school store, where mechanical pencils cost

\$1

\$4

. She can spend up to

\$6

, but not more.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of mechanical pencils Jada will buy

\newline

y =

the number of pens Jada will buy

\newline

\newline

4x + y \leq 6

\newline

x + 4y \leq 6

\newline

4x + y < 6

\newline

x + 4y < 6

At a back-to-school sale at her favorite store, Karen can purchase any pair of pants for

\$17

and any shirt for

\$10

. Her parents tell her that she can spend at most

\$360

on these school clothes.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of pairs of pants

\newline

y =

the number of shirts

\newline

\newline

17x \times 10y \leq 360

\newline

17x + 10y \leq 360

\newline

17x + 10y \geq 360

\newline

17x \times 10y \geq 360

Erik wants to save some low-resolution photos and some high-resolution photos on his flash drive. Each low-resolution photo takes up

1\,\text{MB}

and each high-resolution photo takes up

4\,\text{MB}

. In total, they cannot exceed the total storage space available on the drive, which is

1,970\,\text{MB}

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of low-resolution photos

\newline

y =

the number of high-resolution photos

\newline

\newline

\newline

4 + x + 1 + y \leq 1,970

\newline

x + 4y \leq 1,970

\newline

1 + x + 4 + y \leq 1,970

\newline

4x + y \leq 1,970

Gwen wants to replace the flooring in her house with a combination of carpet and hardwood flooring, but she cannot exceed a budget of

\$4,900

. The carpet she likes has a cost of

\$9

per square foot, and the hardwood flooring she likes has a cost of

\$3

per square foot.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the amount of carpet

\newline

y =

the amount of hardwood flooring

\newline

\newline

\newline

3x + 9y \leq 4,900

\newline

9x + 3y \leq 4,900

\newline

9x + 3y \geq 4,900

\newline

3x + 9y \geq 4,900

Brianna is knitting baby items to sell at a craft fair. She has a total of

1,280

yards of yarn to use for the items. A pair of booties uses

196

yards of yarn and a cap uses

187

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of pairs of booties Brianna can knit

\newline

y =

the number of caps Brianna can knit

\newline

\newline

187x + 196y \leq 1,280

\newline

196x + 187y \leq 1,280

\newline

187x + 196y \geq 1,280

\newline

196x + 187y \geq 1,280

In order to earn some extra money, Maria is mowing lawns. She charges

\$10

to mow a small lawn and

\$28

to mow a large lawn. She would like to make at least

\$110

. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

x =

the number of small lawns

y =

the number of large lawns

\newline

\newline

10x + 28y \geq 110

\newline

28x + 10y \geq 110

\newline

10x + 28y \leq 110

\newline

28x + 10y \leq 110

Alana is selling handmade jewelry to earn money for camp. Bracelets sell for

\$5

and necklaces sell for

\$30

, and she needs to make at least

\$620

in revenue to cover the cost of camp.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of bracelets

\newline

y =

the number of necklaces

\newline

\newline

30x + 5y \geq 620

\newline

30x \times 5y \geq 620

\newline

5x - 30y \geq 620

\newline

5x + 30y \geq 620

As part of a landscaping project, Mr. Ortega is purchasing plants from a garden center. It will cost

\$34

to buy a mature tree, versus

\$8

for a young one. His target is to keep the cost under

\$820

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of mature trees

\newline

y =

the number of young trees

\newline

\newline

34x + 8y < 820

\newline

34x - 8y > 820

\newline

34x + 8y > 820

\newline

34x + 8y < 820

Amelia is designing an exhibit of her paintings and has at most

214

square feet of wall space on which to display them. Her small paintings take up

5

square feet each, and her larger paintings take up

21

square feet each.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of small paintings

\newline

y =

the number of large paintings

\newline

\newline

5x + 21y \leq 214

\newline

5x + 21y \geq 214

\newline

21x + 5y \leq 214

\newline

21x + 5y \geq 214

During the intermission of the school play, the drama class at Danville High School is offering refreshments. The goal is to make more than

\$290

in revenue tonight by selling beverages for

\$1

\$2

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of beverages sold

\newline

y =

the number of snacks sold

\newline

\newline

x + 2y > 290

\newline

1 + x + 2 + y > 290

\newline

1 + x + 2 + y < 290

\newline

x + 2y < 290

Josie wants to save some low-resolution photos and some high-resolution photos on her flash drive. Each low-resolution photo takes up

2\,\text{MB}

and each high-resolution photo takes up

4\,\text{MB}

. In total, they cannot exceed the total storage space available on the drive, which is

80\,\text{MB}

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of low-resolution photos

\newline

y =

the number of high-resolution photos

\newline

\newline

2x + 4y \geq 80

\newline

4x + 2y \leq 80

\newline

2x + 4y \leq 80

\newline

4x + 2y \geq 80

The orchestra in Springdale is putting on a benefit concert for the local children's hospital. Orchestra seating costs

\$43

per ticket and balcony seating is

\$95

. The goal is to raise at least

\$6,100

for the hospital.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of orchestra seats sold

\newline

y =

the number of balcony seats sold

\newline

\newline

\newline

95x + 43y \geq 6,100

\newline

95x + 43y \leq 6,100

\newline

43x + 95y \leq 6,100

\newline

43x + 95y \geq 6,100

Jamal, a costume designer for the Dover City Opera, is making costumes for the chorus members in an upcoming performance. While costuming this group of singers, Jamal must keep costs below

\$1,400

. Male costumes cost

\$6

to make and female costumes cost

\$25

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of male costumes

\newline

y =

the number of female costumes

\newline

\newline

25x - 6y < 1,400

\newline

6x + 25y < 1,400

\newline

6x \times 25y < 1,400

\newline

25x + 6y < 1,400

Gabby is determining the seating arrangement for her big graduation party. Circular tables can seat

10

guests and rectangular tables can seat

9

guests. Together, they must seat at least

141

guests, the number expected.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of circular tables

\newline

y =

the number of rectangular tables

\newline

\newline

10x + 9y > 141

\newline

10x - 9y > 141

\newline

10x \times 9y \geq 141

\newline

10x + 9y \geq 141

Jayla is booking a band and a DJ for a dance, and wants to keep the cost of the entertainment under

\$1,100

. A band can play for part of the time at an hourly rate of

\$120

, and a DJ can play for the remaining time at an hourly rate of

\$80

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of hours the band will play

\newline

y =

the number of hours the DJ will play

\newline

\newline

80 + x + 120 + y < 1,100

\newline

120 + x + 80 + y < 1,100

\newline

120x + 80y < 1,100

\newline

80x + 120y < 1,100

Mrs. Hong is ordering senior portraits of her son to send to their relatives. A medium photo costs

\$12

and a large photo costs

\$34

. She wants to spend less than

\$260

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of medium photos

\newline

y =

the number of large photos

\newline

\newline

34x + 12y < 260

\newline

12x + 34y \leq 260

\newline

12x + 34y < 260

\newline

34x + 12y \leq 260

The Middletown High School softball coach is purchasing equipment for her team. She has a budget of at most

\$770

to purchase bats and softballs. A case of softballs has a price of

\$38

, and a bat has a price of

\$27

. Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

x =

the number of cases of softballs

y =

the number of bats

\newline

\newline

38x - 27y < 770

\newline

38x \times 27y \leq 770

\newline

38x + 27y < 770

\newline

38x + 27y \leq 770

In order to raise money to attend upcoming competitions, the debate team at Belleville High School is selling apple cider and hot chocolate at a basketball game. They hope to make at least

\$170

in revenue at tonight's game, with hot chocolate selling for

\$1

and hot apple cider selling for

\$2

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x

= the number of hot chocolates sold

\newline

y

= the number of apple ciders sold

\newline

\newline

170

\newline

B) \(2x + y \geq

170

\newline

170

\newline

D) x + \(2y \geq

170

Ms. Ellis, the head librarian at the Marshall County Library, can spend at most

\$3,300

to expand the children's section of the library. When she buys from a particular discount seller, paperback books cost

\$2

each and hardback books cost

\$14

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of paperback books

\newline

y =

the number of hardback books

\newline

\newline

14x + 2y \geq 3,300

\newline

2x + 14y \geq 3,300

\newline

2x + 14y \leq 3,300

\newline

14x + 2y \leq 3,300

A charitable organization in Lanberry is hosting a black tie benefit for charity, and the organization's members hope to bring in at least

\$1,600

. Standard tickets are available for

\$16

each, whereas VIP tickets are offered for

\$70

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of standard tickets

\newline

y =

the number of VIP tickets

\newline

\newline

16x + 70y \leq 1,600

\newline

16x + 70y \geq 1,600

\newline

16 + x + 70 + y \leq 1,600

\newline

16 + x + 70 + y \geq 1,600

Logan is buying soda and juice for a party and wants to spend no more than

\$44

\$2

per bottle, and juice costs

\$3

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of bottles of soda

\newline

y =

the number of bottles of juice

\newline

\newline

2x + 3y \leq 44

\newline

2x + 3y < 44

\newline

3x + 2y < 44

\newline

3x + 2y \leq 44

During a special sale, all video games cost

\$28

and all movies cost

\$5

. Hansen plans to spend some or all of his

\$120

in birthday money on these movies and video games.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of video games Hansen can buy

\newline

y =

the number of movies Hansen can buy

\newline

\newline

\newline

28x + 5y \geq 120

\newline

28x + 5y \geq 120

\newline

28x - 5y \leq 120

\newline

28x + 5y \leq 120

As part of a landscaping project, Mr. Kerr is purchasing plants from a garden center. It will cost

\$36

to buy a mature tree, versus

\$8

for a young one. His target is to keep the cost under

\$1,100

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of mature trees

\newline

y =

the number of young trees

\newline

\newline

36x + 8y > 1,100

\newline

36x + 8y < 1,100

\newline

8x + 36y > 1,100

\newline

8x + 36y < 1,100

Cody, the owner of a landscaping company, is ordering rakes and shovels from an equipment wholesaler. He doesn't want to spend more than

\$390

total for his purchases. He can get the rakes at a cost of

\$11

apiece and the shovels at a cost of

\$23

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of rakes ordered

\newline

y =

the number of shovels ordered

\newline

\newline

11x + 23y > 390

\newline

11x + 23y < 390

\newline

11x + 23y \geq 390

\newline

11x + 23y \leq 390

The Dayton Playhouse wants to make at least

\$6,300

on ticket sales this year. Currently, adults' tickets cost

\$58

and children's tickets cost

\$20

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of adults' tickets sold

\newline

y =

the number of children's tickets sold

\newline

\newline

58x + 20y \geq 6,300

\newline

20x + 58y \geq 6,300

\newline

58 + x + 20 + y \geq 6,300

\newline

20 + x + 58 + y \geq 6,300

Isabelle is booking a band and a DJ for a dance, and wants to keep the cost of the entertainment under

\$570

. A band can play for part of the time at an hourly rate of

\$160

, and a DJ can play for the remaining time at an hourly rate of

\$75

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of hours the band will play

\newline

y =

the number of hours the DJ will play

\newline

\newline

160x + 75y < 570

\newline

75x + 160y < 570

\newline

75x + 160y \leq 570

\newline

160x + 75y \leq 570

Mia is going to purchase some writing instruments at the school store, where mechanical pencils cost

\$1

\$3

. She can spend up to

\$12

, but not more.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of mechanical pencils Mia will buy

\newline

y =

the number of pens Mia will buy

\newline

\newline

x + 3y \geq 12

\newline

3x + y \geq 12

\newline

x + 3y \leq 12

\newline

3x + y \leq 12

The Greenville High School softball coach is purchasing equipment for her team. She has a budget of at most

\$590

to purchase bats and softballs. A case of softballs has a price of

\$36

, and a bat has a price of

\$44

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of cases of softballs

\newline

y =

the number of bats

\newline

\newline

44 + x + 36 + y \leq 590

\newline

44x + 36y \leq 590

\newline

36 + x + 44 + y \leq 590

\newline

36x + 44y \leq 590

At a back-to-school sale at her favorite store, Alexa can purchase any pair of pants for

\$22

and any shirt for

\$12

. Her parents tell her that she can spend at most

\$200

on these school clothes.

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of pairs of pants

\newline

y =

the number of shirts

\newline

\newline

12x + 22y \leq 200

\newline

12x + 22y < 200

\newline

22x + 12y \leq 200

\newline

22x + 12y < 200

A software company is hiring some programmers to add to its development team. A junior programmer's salary is

\$51,000

and a senior programmer's salary is

\$78,000

. To keep costs down, the total spending on these new positions must be under

\$960,000

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of junior programmers

\newline

y =

the number of senior programmers

\newline

\newline

51,000x + 78,000y \geq 960,000

\newline

51,000x + 78,000y > 960,000

\newline

51,000x + 78,000y < 960,000

\newline

51,000x + 78,000y \leq 960,000

Simon is sending a fancy organic fruit basket to his grandmother for her birthday. Apples cost

\$3

each, and oranges cost

\$2

each. Simon must stay under his budget of

\$24

\newline

Select the inequality in standard form that describes this situation. Use the given numbers and the following variables.

\newline

x =

the number of apples

\newline

y =

the number of oranges

\newline

\newline

\newline

3x + 2y > 24

\newline

3x + 2y \leq 24

\newline

3x + 2y \geq 24

\newline

3x + 2y < 24