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Solve a system of equations using any method

A utility service company has a fleet of cars and trucks. The gas tank of each car has a volume of

16

gallons, and the gas tank of each truck has a volume of

30

gallons. If it takes

2

000

gallons of gas to fill the empty gas tanks of the entire fleet, which equation shows the possible number of cars,

c

, and number of trucks,

t

, in the fleet?

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1

\newline

16 t+30 c=2,000

\newline

30 t+16 c=2,000

\newline

t+30 c=2,000

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t+16 c=2,000

A manufacturer of pickles has a fixed monthly cost of

\$ 10,000

. Additionally, each jar of pickles that the manufacturer produces costs

\$ 0.75

. If these are the only monthly costs incurred by the manufacturer, which of the following functions best models the manufacturer's total monthly cost,

C

, when it produces

p

jars of pickles?

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1

\newline

C(p)=10,000+0.75 p

\newline

C(p)=0.75+10,000 p

\newline

C(p)=10,000 \cdot 0.75 \cdot p

\newline

C(p)=0.75(10,000+p

A professional baseball team sells regular tickets and premium tickets to all of its home games. At a recent game, the average price for a regular ticket was

\$ 52.46

, and the average price for a premium ticket was

\$ 175.85

. Which of the following equations shows a relationship where the number of regular tickets,

r

, and the number of premium tickets,

p

, that the team sells generates

\$ 5,000,000

in ticket sales?

\newline

1

\newline

\frac{p}{52.46}+\frac{r}{175.85}=5,0 c

\newline

\frac{r}{52.46}+\frac{p}{175.85}=5,0 \mathrm{C}

\newline

52.46 p+175.85 r=5,01

\newline

52.46 r+175.85 p=5,01

When Lúcia plays golf at the Rolling Hills golf course, she loses about

12

balls on average. When she plays golf at the Meandering Meadows golf course, she loses about

8

balls on average. If Lúcia lost approximately

100

balls after playing at Rolling Hills

r

times and at Meandering Meadows

m

times, which of the following equations best represents the relationship between

r

m

\newline

1

\newline

8 r+12 m=100

\newline

12 r+8 m=100

\newline

12 r-8 m=100

\newline

8 r-12 m=100

A clothier who only makes shirts and pants can make a shirt in

4

hours and a pair of pants in

6

hours. Which of the following equations shows the number of shirts,

s

, and the number of pants,

p

, that the clothier can make in a

40

hour work week?

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1

\newline

6 s+4 p=40

\newline

4 s+6 p=40

\newline

\frac{s}{4}+\frac{p}{6}=40

\newline

\frac{s}{6}+\frac{p}{4}=40

A farmer's rectangular plot with a length of

l

meters and a width of

w

meters is shown in the figure. The perimeter, or distance around the plot, is

700

meters. Which of the following equations shows the perimeter of the plot in terms of length and width?

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1

\newline

2 l+2 w=700

\newline

2 l+2 w=350

\newline

l+w=700

\newline

l w=700

A cashier counts

\$ 15.75

in quarters and dimes at the end of a workday. Which of the following equations shows the relationship between the number of quarters,

q

d

, that the cashier counted?

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1

\newline

\frac{0.25}{q}+\frac{0.10}{d}=15.75

\newline

\frac{q}{0.25}+\frac{d}{0.10}=15.75

\newline

0.35(q+d)=15.75

\newline

0.25 q+0.10 d=15.75

D=27.4 m+12,100

\newline

D

, in millions of miles, of the Voyager

1

spacecraft from the Sun

m

months after January

1

2015

is approximated by the equation. What is the best interpretation of

27

4

as shown in the given equation?

\newline

1

\newline

1

27

4

months before January

1

2015

\newline

(B) The Voyager

1

27

4

million miles per hour.

\newline

(C) The Voyager

1

was a distance of

27

4

million miles from the Sun on January

1

2015

\newline

(D) The distance between Voyager

1

and the Sun increases by

27

4

million miles every month.

\newline

linear relationships | Lesson

T=0.25 q+87

\newline

Manon's statistics professor puts a bonus question on every test, which adds

0

25

points to a student's overall grade at the end of the term. The equation gives Manon's current overall grade,

T

, after taking into account

q

extra credit questions answered correctly. What does the

87

mean in this equation?

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1

\newline

(A) Manon must get an

87

or above to pass.

\newline

(B) Manon's average is an

87

before adding the extra credit.

\newline

(C) After adding in her extra credit, Manon's average is an

87

\newline

(D) Manon's professor gave

87

opportunities for extra credit this term.

\newline

linear relationships | Lesson

When Li Juan's auto yard is filled to capacity with only cars, it has

60

cars. When it is filled to capacity with only vans, it has

50

vans. Which linear equation models the number of cars,

c

v

, that could be in Li Juan's auto yard when it is filled to capacity?

\newline

1

\newline

\frac{c}{60}+\frac{v}{50}=1

\newline

60 c+50 v=1

\newline

\frac{c}{50}+\frac{v}{60}=1

\newline

50 c+60 v=1

Noah is having his driveway resurfaced, which costs

\$ 25

per square meter. The driveway will also be given new edging around its perimeter, which costs

\$ 6.50

a

be the area, in square meters, of the driveway; and let

c

be the total cost of resurfacing the driveway and installing the new edging. If the perimeter of the driveway is

36

meters, which of the following equations correctly relates

a

c

\newline

1

\newline

a=234-25 c

\newline

c=234-25 a

\newline

a=234+25 c

\newline

c=234+25 a

A forest that is populated by crows and doves currently contains a total of

1

500

crow and dove nests. Crows use approximately

8

grams of twigs when building a nest, and doves use approximately

6

grams of twigs when building a nest. Which of the following equations best approximates the relationship between

C

, the total amount, in grams, of twigs used for crow nests and

D

, the total amount, in grams, of twigs used for dove nests?

\newline

1

\newline

\frac{C}{8}+\frac{D}{6}=1,500

\newline

\frac{C}{6}+\frac{D}{8}=1,500

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6 C+8 D=1,500

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8 C+6 D=1,500

Elon is purchasing materials for a gardening project. Mulch costs

\$ 33

per cubic yard. Edge material costs

\$ 60

5

yards. Elon needs

60

yards worth of edge material. Let

v

be the volume, in cubic yards, of mulch that Elon buys; and let

c

be the total cost, in dollars, of his purchase. Which of the following equations correctly relates

v

c

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1

\newline

33 v+720=c

\newline

33 v+1,980=c

\newline

33 v+3,600=c

\newline

33 v+18,000=c

Dew point temperature, in degrees Celsius

\left({ }^{\circ} \mathrm{C}\right)

, is defined as the temperature to which the air would have to cool in order to reach saturation. For a temperature of

35^{\circ} \mathrm{C}

, an estimate of the dew point can be obtained by first subtracting

20^{\circ} \mathrm{C}

from the temperature, and then adding

1^{\circ}

for every increase of

5

points in the relative humidity,

R

. If the dew point is

30^{\circ} \mathrm{C}

, which of the following equations best models the situation?

\newline

1

\newline

30=15-\frac{1}{5} R

\newline

30=15+5 R

\newline

30=15-5 R

\newline

30=15+\frac{1}{5} R

A landscaping company sells bags that hold up to

2

3

\left(\mathrm{ft}^{3}\right)

of mulch. The company guarantees that there is at least

2 \mathrm{ft}^{3}

of mulch inside each bag. Which of the following functions gives the nonnegative difference between the maximum and minimum mulch volumes, in cubic feet, that could be contained in

b

bags purchased from the landscaping company?

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1

\newline

f(b)=0.3 b

\newline

f(b)=2 b

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f(b)=2.3 b

\newline

f(b)=4.3 b

Jacob's classroom contains tables and chairs, each with

4

legs. Jacob puts a pad on the end of every leg so that the tables and chairs will not make noise when they are moved around. If Jacob needs exactly

80

pads for his classroom, which of the following equations correctly relates the number of chairs,

c

, to the number of tables,

t

\newline

1

\newline

c=80-4 t

\newline

c=80-t

\newline

c=20-4 t

\newline

c=20-t

A charging station can only charge cell phones and laptops. Cell phones use approximately

3

joules per second

\left(\frac{\mathrm{J}}{\mathrm{s}}\right)

when charging, and laptops use approximately

40 \frac{\mathrm{J}}{\mathrm{s}}

when charging. Which of the following equations represents the relationship between the number of cell phones,

c

, and the number of laptops,

l

, that could be charging when the station's output is exactly

160 \frac{\mathrm{J}}{\mathrm{s}}

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1

\newline

c=-40 l+160

\newline

c=-\frac{40}{3} l+\frac{160}{3}

\newline

c=-3 l+160

\newline

c=-\frac{3}{40} l+\frac{160}{40}

Aaron is purchasing party hats and fake mustaches for an end of the school year party. He can spend at most

\$ 30

. Fake mustaches cost

\$ 3

each, and party hats cost

\$ 2

each. If he must purchase a combination of at least

15

mustaches and party hats, which of the following systems of inequalities best models the relationship between the number of mustaches,

m

, and party hats,

p

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1

\newline

\left\{\begin{array}{l}m+p \geq 15 \\ 3 m+2 p \leq 30\end{array}\right.

\newline

\left\{\begin{array}{l}m+p \leq 15 \\ 3 m+2 p \geq 30\end{array}\right.

\newline

\left\{\begin{array}{l}3 m+2 p \geq 15 \\ m+p \leq 30\end{array}\right.

\newline

\left\{\begin{array}{l}3 m+2 p \leq 15 \\ m+p \geq 30\end{array}\right.

The equation of a circle is

(x-2)^{2}+(y+4)^{2}=36

. What are the center and radius of the circle?

\newline

1

\newline

(A) The center is

(2,4)

and the radius is

6

\newline

(B) The center is

(2,-4)

and the radius is

6

\newline

(C) The center is

(-2,-4)

and the radius is

6

\newline

(D) The center is

(2,-4)

and the radius is

36

A teacher purchased

300

colored pencils for an upcoming project. The pencils she ordered come in packs of

20

30

14

packs in all. Write a system of equations to find the number of

20

(x)

30

(y)

the art teacher ordered.

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

\newline

There are two mystery numbers. The sum of

3

times the first number and

3

times the second number is

-18

2

times the first number and

3

times the second number is

-13

. What are the two numbers?

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The first number is ______ , and the second number is ______.

\newline

y = -1

\newline

-2x - 4y = 8

\newline

(_____ , _____)

...