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Solve a system of equations using substitution: word problems

P=67,000+2,820 m

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The total payments,

P

, in dollars, made by a homeowner

m

months after starting payments on a home mortgage is given by the equation. What is the best interpretation of

67

000

as shown in the given equation?

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1

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A The first payment was

67

000

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(B) The homeowner pays

67

000

dollars each month.

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(C) The homeowner paid

67

000

dollars at the end of the first month.

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D The total of all payments made by the homeowner is

67

000

C=16,500+130 m

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The total cost,

C

, in dollars, to purchase a planchet machine and use it for

m

months is given by the equation. What is the best interpretation of

130

as shown in the given equation?

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1

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(A) The cost increase by

130

dollars for each additional month of use.

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B The cost to purchase the machine and not use it is

130

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(C) After purchase, the machine can be used for up to

130

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D) The average cost per month to purchase and use the machine is

130

Today, the population of Canyon Falls is

22

500

and the population of Swift Creek is

15

200

. The population of Canyon Falls is decreasing at the rate of

740

people each year while the population of Swift Creek is increasing at the rate of

1

500

people each year. Assuming these rates continue into the future, in how many years from today will the population of Swift Creek equal twice the population of Canyon Falls?

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1

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9

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10

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11

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12

A company produces candy bags that each hold about

528

cubic inches of candy. Each bag is filled with any mixture of lollipop candies and gummy bear candies. When a bag contains only lollipop candies, then it has about

361

candies. When a bag contains only gummy bear candies, then it has about

697

candies. Given any candy bag produced by this company, which of the following equations could relate the approximate number of lollipop candies,

l

, in the bag and the approximate number of gummy bear candies,

g

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1

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\frac{l}{361}+\frac{g}{697}=528

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361 l+697 g=528

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\frac{l}{361}+\frac{g}{697}=1

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361 l+697 g=1

A jar of jelly bean candies weighs

8

ounces. A container of caramel candies weighs

40

ounces. Lúcia buys

10

pounds worth of jelly bean candy jars and caramel candy containers for her big party. Given that there are

16

ounces in a pound, which of the following equations correctly relates the number of jars of jelly bean candies,

j

, and the number of containers of caramel candies,

c

, that Lúcia bought?

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1

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\frac{8}{16} j+\frac{40}{16} c=10

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8 j+40 c=10

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\frac{16}{8} j+\frac{16}{40} c=10

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16 \cdot 8 j+16 \cdot 40 c=10

C=1,500 n+1,000

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C

, in dollars, to ship

n

cars from Europe to the United States is given in the equation. What is the difference, in cost, to ship

7

6

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1

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\$ 500

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\$ 1,000

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\$ 1,500

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\$ 2,500

Jelani needs to hire at least

12

artists for an upcoming event. He needs to hire visual artists, who will be paid

\$ 300

for the event, and performers, who will be paid

\$ 480

for the event. His budget for paying the artists is no more than

\$ 6,000

. He must hire at least

4

visual artists and at least

3

performers. Which of the following does not satisfy all of the conditions described?

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1

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4

visual artists and

10

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8

visual artists and

8

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9

visual artists and

3

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13

visual artists and

4

A rectangular garden has a length of

60

\mathrm{ft}

w

\mathrm{ft}

, and a perimeter of

200

\mathrm{ft}

. Which of the following equations best models the garden's perimeter?

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1

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60+w=200

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60+2 w=200

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120+w=200

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120+2 w=200

A grocery store sells

5

-pound bags of beans for

\$ 6

10

-pound bags of rice for

\$ 15

each. Taye wants to buy at least as many pounds of rice as he buys of beans. He wants to spend at least

\$ 60

, and he can carry a maximum of

55

pounds. Which of the following purchases satisfies all of Taye's conditions?

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1

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3

bags of beans and

6

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4

bags of beans and

2

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4

bags of beans and

3

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6

bags of beans and

2

Write a system of equations to describe the situation below, solve using substitution, and fill in the blanks.

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Last Wednesday, two friends met up after school to read the book they were both assigned in Literature class. Bryan can read

2

pages per minute, and he had already read

98

pages. Jayla, who has a reading speed of

3

pages per minute, had read

48

pages. Eventually they had read the same number of pages. How long did that take? How many pages had each of them read?

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minutes, Bryan and Jayla had each read

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