PSAT Math Grid-Ins Question 56: Answer and Explanation

Question: 56

Daniel works for a pest control company and is spraying all the lawns in a neighborhood. The figure above shows the layout of the neighborhood and the times that Daniel started spraying the lawns at two of the houses. Each lawn in the neighborhood is approximately 0.2 acres in size and takes the same amount of time to spray.

Daniel uses a mobile spray rig that holds 20 gallons of liquid. It takes 1 gallon to spray 2,500 square feet of lawn. How many times, including the first time, will Daniel need to fill the spray rig, assuming he fills it to the very top each time? (Note: 1 acre = 43,560 square feet.)

Correct Answer: 4

Explanation:

4

Difficulty: Hard

Category: Problem Solving and Data Analysis/Rates, Ratios, Proportions, and Percentages

Getting to the Answer: This part of the question contains several steps. Think about the units given in the question and what you need to convert so that you can get to the answer. The total acreage of all the lawns in the neighborhood is 21 × 0.2 = 4.2 acres. This is equivalent to 4.2 × 43,560 = 182,952 square feet. Each gallon of spray covers 2,500 square feet, so divide to find that Daniel needs 182,952 ÷ 2,500 = 73.1808 gallons to spray all the lawns. The spray rig holds 20 gallons, so Daniel will need to fill it 4 times. After he fills it the fourth time and finishes all the lawns, there will be some spray left over.