Mr. Malone used 40 pounds of insecticide to cover 1,760 square feet of lawn and 60 pounds to cover an additional 2,640 square feet. how many pounds of insecticide would Mr. Malone need to cover his whole lawn of 4,480 square feet?
The Correct Answer and Explanation is:
To determine how many pounds of insecticide Mr. Malone needs to cover his entire 4,480 square foot lawn, we can use the relationship between the amount of insecticide and the area it covers. This problem involves finding the rate of insecticide application (in pounds per square foot) and then applying that rate to the entire lawn.
Step 1: Calculate the rate of insecticide per square foot
We are given two areas with corresponding amounts of insecticide used:
- 40 pounds of insecticide for 1,760 square feet
- 60 pounds of insecticide for 2,640 square feet
To find the rate of insecticide application, we divide the number of pounds by the area it covers for each section:
- For the first area:
Rate = ( \frac{40 \text{ pounds}}{1,760 \text{ square feet}} = 0.0227 \text{ pounds per square foot} ) - For the second area:
Rate = ( \frac{60 \text{ pounds}}{2,640 \text{ square feet}} = 0.0227 \text{ pounds per square foot} )
As we can see, the rate of insecticide application is consistent in both cases: 0.0227 pounds per square foot.
Step 2: Calculate the total pounds of insecticide needed
Now, we can use the consistent rate of insecticide application to find out how many pounds are needed for the entire lawn of 4,480 square feet. Using the rate of 0.0227 pounds per square foot, we multiply the total area by the rate:
[
\text{Total insecticide needed} = 4,480 \text{ square feet} \times 0.0227 \text{ pounds per square foot}
]
[
\text{Total insecticide needed} = 101.856 \text{ pounds}
]
Since the amount of insecticide should be rounded to the nearest pound, Mr. Malone would need approximately 102 pounds of insecticide to cover his entire 4,480 square foot lawn.
Final Answer:
102 pounds of insecticide are required to cover the entire lawn.
Explanation:
This problem involved first calculating the rate at which insecticide was applied per square foot. By using the same rate for the entire lawn, we can determine how many pounds of insecticide Mr. Malone needs for the total area. The consistent application rate simplifies the problem, making it possible to calculate the required insecticide for any lawn size.