You are applying fertilizer to a football field. The field is 360 feet long and 160 feet wide. You use 8 pounds of fertilizer per 1,000 square feet. The fertilizer comes in 50-pound bags. How many bags of fertilizer will you need to complete the job?
The Correct Answer and Explanation is
Correct Answer: 10 Bags
Step-by-Step Explanation:
You’re tasked with fertilizing a football field that is 360 feet long and 160 feet wide. You are told:
- The application rate is 8 pounds per 1,000 square feet.
- Fertilizer comes in 50-pound bags.
1. Calculate the total area of the football field:
Area=Length×Width=360 ft×160 ft=57,600 square feet\text{Area} = \text{Length} \times \text{Width} = 360 \, \text{ft} \times 160 \, \text{ft} = 57,600 \, \text{square feet}
2. Determine how many units of 1,000 square feet are in the total area:
57,6001,000=57.6\frac{57,600}{1,000} = 57.6
This means the field consists of 57.6 units of 1,000 square feet.
3. Calculate the total amount of fertilizer needed (in pounds):
Since 8 pounds are needed per 1,000 square feet: 8×57.6=460.8 pounds of fertilizer8 \times 57.6 = 460.8 \, \text{pounds of fertilizer}
4. Determine how many 50-pound bags are required:
Each bag contains 50 pounds of fertilizer. Divide the total pounds needed by 50: 460.850=9.216\frac{460.8}{50} = 9.216
Since you can’t purchase a fraction of a bag, you must round up to the next whole number. ⌈9.216⌉=10 bags\lceil 9.216 \rceil = 10 \, \text{bags}
Final Answer: You will need 10 bags of fertilizer.
Summary:
This problem requires multiplication, unit rate application, and practical rounding. The football field has an area of 57,600 square feet. At 8 pounds of fertilizer per 1,000 square feet, the total fertilizer needed is 460.8 pounds. Since fertilizer is sold in 50-pound bags, divide to find the number of bags. The result (9.216) is rounded up to 10 bags to ensure complete coverage of the field.