Practice questions
- Tysha went to the bookstore and purchased $626.15 worth of books. Paperback books cost $15.95 each, and hardcover books cost $27.95 each. She purchased a total of 37 books, so how many of them were paperbacks?
A. 34 B. 30 C. 12 D. 28
- Olivia must mix a 20 percent concentrate with a mixture that has a 60 percent concentration to get 80 gallons of a mixture with a concentration of 30 percent. How many gallons of the 20 percent concentrate does Olivia need?
A. 24 gallons B. 48 gallons C. 70 gallons D. 60 gallons
Answers and explanations
- The correct answer is Choice (A).
As with most mixture word problems, it's easiest to create a table. Let p represent the number of paperbacks Tysha bought, because they cost less than hardcovers do.
Create an equation using the "Total" column:
Tysha bought 34 paperbacks. The remaining three were hardcovers.
- The correct answer is Choice (D).
Define your variable first. Let x represent the number of gallons Olivia needs from the 20 percent concentrate. That means 80 – x will represent the number of gallons she needs of the 60 percent concentrate.
A table can help you visualize the problem:
You don't know what belongs where the "Total" row and the "Total" column intersect. If you multiply across the "Total" row, the answer is 24, so that goes on one side of your equation. Add down the "Total" column and put the sum on the other side of the equation:
Olivia needs 60 gallons of the 20 percent concentrate to make her solution.