Question 1

Which of the following correctly translates the phrase "five less than twice a number x" into an algebraic expression?

Accepted Answer

$$2x - 5$$

Question 2

A rectangle's length is 8 feet shorter than double its width. Which equation represents the relationship between the length $$l$$ and width $$w$$?

Accepted Answer

$$l = 2w - 8$$

Question 3

Amanda is three times older than her brother. If $$x is $$her brother's age, which equation models Amanda's age?

Accepted Answer

$$a = 3x$$

Question 4

A triangle has two sides that are equal in length and a third side that is 3 inches shorter than one and one-half times the length of the equal sides. If the perimeter is 28.5 inches, which equation represents the situation if $$x is $$the length of the equal sides?

Accepted Answer

$$2x + (1.5x - 3) = 28.5$$

Question 5

The Smithfield City Parking Garage charges $$6 for the first hour and 3 $$for each additional hour. If a car is parked for $$n$$ hours, which equation gives the total cost $$C$$?

Accepted Answer

$$C = 6 + 3(n - 1)$$

Question 6

If the phrase "the quotient of $$x$$ and $$y$$" is translated into a mathematical expression, which is correct?

Accepted Answer

$$\frac{x}{y}$$

Question 7

A chemical solution contains a volume $$v$$ that is 12 milliliters less than three times the volume $$w of $$another solution. Which equation models this relationship?

Accepted Answer

$$v = 3w - 12$$

Question 8

Which of the following is the correct symbolic equivalent for the English phrase "the sum of $$a$$ and $$b$$"?

Accepted Answer

$$a + b$$

Question 9

A triangle has two equal sides of length $$x$$ and a third side that is $$5$$ inches shorter than twice the length of the equal sides. If the perimeter is $$31$$ inches, what is the value of $$x$$?

Accepted Answer

$$x = 9$$

Question 10

A parking garage charges $$8 for the first hour and 4 $$for each additional hour. If a car is parked for $$5$$ hours, what is the total cost?

Accepted Answer

$$24$$

Question 11

Which of the following is the correct translation for "twice the sum of $$x$$ and $$y$$"?

Accepted Answer

$$2(x + y)$$

Question 12

A rectangle's width is $$w$$ and its length is $$l = w + 7. If $$the perimeter is $$38$$ units, what is the value of $$w$$?

Accepted Answer

$$w = 6$$

Question 13

If the phrase "the product of $$a$$ and $$b$$" is translated into a mathematical expression, which is correct?

Accepted Answer

$$ab$$

Question 14

A triangle has two equal sides of length $$x$$ and a third side that is $$2$$ inches longer than the equal sides. If the perimeter is $$32$$ inches, what is the value of $$x$$?

Accepted Answer

$$x = 10$$

Question 15

Which equation represents "the difference between $$x$$ and $$y is $$equal to 12"?

Accepted Answer

$$x - y = 12$$

Question 16

A rectangle has a length that is 4 times its width. If the perimeter is 50 units, what is the width?

Accepted Answer

$$w = 5$$

Question 17

Which of the following is the correct translation for "the sum of twice $$x$$ and three times $$y$$"?

Accepted Answer

$$2x + 3y$$

Question 18

A parking garage charges $$7 for the first hour and 2 $$for each additional hour. If a car is parked for $$n$$ hours, which equation gives the total cost $$C$$?

Accepted Answer

$$C = 7 + 2(n - 1)$$

Question 19

Which equation represents "the quotient of $$x$$ and the sum of $$y$$ and $$z$$"?

Accepted Answer

$$\frac{x}{y + z}$$

Using Equations to Solve Word Problems: Translating and Solving in College Algebra

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