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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