To review these concepts, go to Introduction to Algebra Word Problems Study Guide.
Introduction to Algebra Word Problems Practice Questions
Practice
Find the answer to each question.
 Every week, Natalie swims three more than six times the number of laps Michael swims. If Natalie swims 45 laps, how many laps does Michael swim?
 Josh fills 60 cups of water from a 500–ounce water cooler. If there are 20 ounces left in the cooler when Josh has finished, and each cup contains the same amount of water, how much water is in each cup?
 Tanya has $25 in her bank. She adds to the bank one–fifth of the money she receives for her birthday, bringing the total to $41. How much money did Tanya receive for her birthday?
 A gym has a membership fee of $50 and a monthly fee of $30. If Angela has $200, for how many months could she belong to the gym?
 Tatiana needs $150 to go to camp. She has $38 saved, and she sells raffle tickets for $4 each. How many tickets must she sell in order to go to camp?
Solutions

We are looking for the number of laps Michael swims, so we can use x to represent that number. Natalie swims three more than six times that number, which means that she swims 6x + 3 laps. We know that she swims 45 laps, so we can set 6x + 3 equal to 45 and solve for x:
6x + 3 = 45
6x = 42
x = 7
Michael swims 7 laps.

We're looking for the volume of water in each cup, so we can use x to represent that number. Josh fills 60 cups with water, so 60 times x, or 60x, is equal to the amount of water used to fill the cups. The cooler has 20 ounces left after the cups are filled, which means that the amount of water in the cups, 60x, plus 20 is equal to 500:
60x + 20 = 500
60x = 480
x = 8
Each cup of water contains 8 ounces.

We're looking for the amount of money Tanya received for her birthday, so we can use x to represent that number. She adds to the bank one–fifth of what she received. Divide what she received, x, by 5: . She had $25 in her bank already, so add 25 to . The total is equal to the total in her bank now,$41:
+ 25 = 41
= 16
x = 80
Tanya received $80 for her birthday.

We're looking for the number of months Angela could belong to the gym, so use x to represent that number. There is a maximum number of months Angela could belong to the gym, but she could also belong to the gym for a shorter period of time, so we need an inequality. The monthly fee is $30, so the amount of money spent in monthly fees is 30 times the number of months, or 30x. Angela must also pay the membership fee, $50, and the total of the monthly fee and the membership fee must be less than or equal to the amount of money Angela has, $200:
30x + 50 ≤ 200
30x ≤ 150
x ≤5
Angela can belong to the gym for 5 or fewer months.

We're looking for the number of tickets Tatiana must sell, so we can use x to represent that number. There is a minimum number of tickets Tatiana must sell, but she could also sell more than that number, so we need an inequality. Each raffle ticket costs $4, so the amount of money Tatiana collects is equal to 4 times the number of tickets she sells, or 4x. She already has $38, so the total money collected from selling tickets plus that $38 must be greater than or equal to the cost of going to camp, $150:
4x + 38 ≥ 150
4x ≥ 112
x ≥ 28
Tatiana must sell 28 or more tickets to go to camp.
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