Free Printable Heart of Algebra - Linear Equations and Linear Word Problems

1.

Suppose $\frac{8-x}{7}=10$ . What is the value of x?

a)

-62

b)

-14

c)

14

d)

62

2.

Suppose $2x-9=-15$ . What is the value of x?

a)

-11

b)

-3

c)

3

d)

11

3.

Solve for x.

$ax+bc=d$

a)

$x=\frac{d-bc}{a}$

b)

$x=\frac{d}{a}-bc$

c)

$x=\frac{d-a}{bc}$

d)

$x=\frac{d}{bc}-a$

4.

Solve for x.

$\frac{x}{a}+b=c$

a)

$x=a\left(c-b\right)$

b)

$x=ac-b$

c)

$x=\frac{c}{b}-a$

d)

$x=\frac{c}{b-a}$

5.

Tanya tracks the number of guppies in her fish tank during the month of September. After some analysis, she concludes that the population of guppies in her tank, P, w weeks into September, can be modeled by the equation

P=4w+7

Which of the following best explains what the 7 means in the context of this situation?

a)

It is the number of guppies in the tank when Tanya began tracking the guppy population.

b)

It is the number of guppies added to the tank per week.

c)

It is the number of ounces of food Tanya must add to make sure all the fish are adequately fed.

d)

It is the number of weeks Tanya will be tracking the guppy population.

6.

Jamison is trying out a new diet in order to lose weight. To determine the diet's effectiveness, Jamison keeps a journal where he tracks his weight on a weekly basis. He determines that, in his first two months on the diet, his weight can be modeled by the equation

W=-2.5t+195

where W is his weight in pounds and t is the time in weeks since he started journaling. Which of the following best describes what the -2.5 means in the context of this situation?

a)

It is the weight Jamison loses per week.

b)

It is Jamison's starting weight.

c)

It is the number of hours Jamison must exercise per week in order to maintain his weight loss.

d)

It is the amount of time in weeks it takes for him to lose one pound.

7.

A climatologist is tracking the number of species of birds living near a river delta to measure the effects of climate change. When she begins her study, there are a total of 50 different species of birds living near the delta. She notices that the number of species of birds decreases by 3 every year. Which of the following equations models the number of species of birds living in the delta, S, t years after the climatologist began her study?

a)

$S=-3t+50$

b)

$S=3t-50$

c)

$S=-50t+3$

d)

$S=50t-3$

8.

A grocery store manager notices that the number of patrons entering the store increases based on the number of coupons discounting items more than 50%. Without any of these coupons, the store usually sees 310 patrons per day. Which of the following equations could represent the number of patrons in the store, P, when there are c coupons discounting items more than 50%?

a)

$P=25c+310$

b)

$P=-25c+310$

c)

$P=310-25c$

d)

$P=-\frac{1}{2}c+310$

9.

Which of the following is the equation for the line passing through the points (0,5) and (8,10)?

a)

$y=\frac{5}{8}x+5$

b)

$y=\frac{8}{5}x+5$

c)

$y=\frac{4}{5}x+5$

d)

$y=\frac{5}{4}x+5$

10.

For her New Year's Resolution, Donna wants to read more books. To see how well she's doing, Donna tracks when she finishes each book in a list. By April, Donna has read a total of 6 books. Assuming Donna had 0 books read at the beginning of the year, that April represents the fourth month, and that Donna continues to read at the same rate for the rest of the year, which of the following equations represents the number of books Donna has read, B, m months into the year?

a)

$y=\frac{3}{2}x$

b)

$y=4x$

c)

$y=x+4$

d)

$y=4x+6$

Heart of Algebra - Linear Equations and Linear Word Problems

Total questions: 10

Worksheet time: 20mins

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