Question 1

A car is currently valued at $24,000 and depreciates by $2,000 each year. Which equation models the car's value $y$ after $x$ years?

Accepted Answer

$y = 24,000 - 2,000x$

Question 2

Solve for $w$ in the formula $P = 2l + 2w$.

Accepted Answer

$w = \frac{P - 2l}{2}$

Question 3

If $x + y = 32$ and $y = x + 20$, what is the value of $x$?

Accepted Answer

$x = 6$

Question 4

You invest $15,000$ in two accounts, one paying $2\%$ and the other $6\%$ annual interest. If the total interest earned in one year is $710$, how much was invested at $6\%$?

Accepted Answer

$3,000$

Question 5

Which of the following is the correct formula for simple interest?

Accepted Answer

$I = Prt$

Question 6

A rectangle has a perimeter of $382$ units and its length is $7$ units more than three times its width. What is the width?

Accepted Answer

$w = 46$

Question 7

If $y = 32 - 20$, what is the value of $y$?

Accepted Answer

$y = 12$

Question 8

Given the formula $P = C + mC$, solve for $C$.

Accepted Answer

$C = \frac{P}{1 + m}$

Question 9

A bachelor's degree takes $x$ years and a master's degree takes $42 - 2x$ years. If the total time for both is $123$ years, how many years does the bachelor's degree take?

Accepted Answer

$x = 71$

Question 10

If a price is reduced by $8\%$ and the new price is $21,160$, what was the original price?

Accepted Answer

$x = 23,000$

Question 11

Which step should you do first when solving a word problem using linear equations?

Accepted Answer

Identify what the question is asking for

Question 12

If $2x + 20 = 32$, what is the value of $x$?

Accepted Answer

$x = 6$

Question 13

A club has $y$ members now and loses $200$ members per year. If it had $2,900$ members $x$ years ago, which equation models the current membership?

Accepted Answer

$y = 2,900 - 200x$

Question 14

If $x + (x + 20) = 32$, what is the value of $x$?

Accepted Answer

$x = 6$

Question 15

If $P = 2l + 2w$ and $P = 382$, $l = 7 + 3w$, what is the value of $w$?

Accepted Answer

$w = 46$

Question 16

If $I = Prt$ and $P = 2,500$, $r = 0.02$, $t = 1$, what is the interest earned?

Accepted Answer

$I = 50$

Linear Equations and Applications: College Algebra Study Notes

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