Praxis Core Academic Skills for Educators: Mathematics (5733)Number and QuantityMedium
A gardener is mixing soil for a new plant bed. He uses 3 parts topsoil, 2 parts compost, and 1 part sand. If he needs a total of 72 cubic feet of soil mix, how many cubic feet of compost does he need?
- A18 cubic feet
- B24 cubic feet
- C12 cubic feet
- D36 cubic feet
Show answer & explanationAnswer & explanation
Correct answer: B. 24 cubic feet
First, find the total number of parts in the ratio. Then, determine the value of one part by dividing the total volume by the total parts. Finally, multiply the value of one part by the number of parts for compost.
Why the other options are wrong
- A. This is 1/4 of total volume, not 2/6.
- C. This would be the amount of sand (1 part).
- D. This is the amount of topsoil (3 parts), not compost.
Ratio and Total Quantity
When a total quantity is divided into parts according to a ratio, sum the ratio parts to find the total parts. Divide the total quantity by the total parts to find the value of one part, then multiply by each ratio component.
- Ratios express relative proportions.
- Summing ratio components gives the total 'parts'.
- Each part's quantity is found by multiplying its ratio component by the 'value per part'.
Memory trick: Divide total by parts, then multiply for each share.