Many students struggle when it comes to solving word problems. In order to really understand how to set up and solve a word problem, our first task is to be able to translate between a given phrase and the corresponding algebraic expression.

Test Objectives
• Demonstrate the ability to translate between a given phrase and an algebraic expression
• Demonstrate the ability to solve a basic word problem with linear equations
Translating Phrases to Expressions Practice Test:

#1:

Instructions: solve each word problem.

a) If the difference of a number and 1 is multiplied by 2, the result is the same as 3 less than 5 times the number. Find the number.

#2:

Instructions: solve each word problem.

a) If 2 is added to 5 times a number, the result is the same as 5 more than 4 times the number. Find the number.

#3:

Instructions: solve each word problem.

a) If the difference of 3 times a number and 7 is multiplied by 5, the result is the same as 5 less than 6 multiplied by the difference of the number and 2. Find the number.

#4:

Instructions: solve each word problem.

a) The quotient of a number and 9 is the same as 2 times the difference of the number and 1. Find the number.

#5:

Instructions: solve each word problem.

a) If the quotient of a number and 5 is added to 3, the result is the same as 12/5 being subtracted away from 2 times the sum of the number and 9. Find the number.

Written Solutions:

#1:

Solutions:

$$a)\hspace{.2em}\frac{1}{3}$$

#2:

Solutions:

$$a)\hspace{.2em}3$$

#3:

Solutions:

$$a)\hspace{.2em}2$$

#4:

Solutions:

$$a)\hspace{.2em}\frac{18}{17}$$

#5:

Solutions:

$$a)\hspace{.2em}-7$$