Question

Noah charges $20 for each lawn that he mows. Answer the questions below.

Answer 1

After 20 hours, there are 1326 acres left to mow; after 100 hours, 1230 acres are left; and it takes 1125 hours to mow all lawns.

Step-by-step explanation:

The question involves the use of a linear equation to determine the acreage of land left to mow after a given number of hours, as well as solving for the number of hours needed to mow the entire area. The equation given is ý = 1350 - 1.2x, where x represents the number of hours of work and ý represents the number of acres left to mow. To find answers to the questions, we just need to substitute the value of x and solve for ý.

31. Acres left after 20 hours of work:

To find the acres left to mow after 20 hours of work, we substitute x = 20 into the equation:

ý = 1350 - 1.2(20)

ý = 1350 - 24

ý = 1326 acres left to mow

32. Acres left after 100 hours of work:

Substitute x = 100 into the equation:

ý = 1350 - 1.2(100)

ý = 1350 - 120

ý = 1230 acres left to mow

33. Hours to mow all the lawns:

To find the time it takes to mow all the lawns, or when ý = 0, set the equation to zero and solve for x:

0 = 1350 - 1.2x

1.2x = 1350

x = 1125 hours to mow all lawns

Answer 2

To find the number of acres left to mow after a certain number of hours, substitute the value of x into the equation ŷ = 1350 - 1.2x. After 20 hours, there are 1326 acres left to mow. After 100 hours, there are 1230 acres left to mow. It takes approximately 1125 hours to mow all the lawns.

Step-by-step explanation:

To find the number of acres left to mow after a certain number of hours, we can substitute the value of x (number of hours) into the equation ŷ = 1350 - 1.2x. For example, after 20 hours of work, we substitute x = 20 into the equation. ŷ = 1350 - 1.2(20) = 1350 - 24 = 1326 acres left to mow. After 100 hours of work, substituting x = 100, we get ŷ = 1350 - 1.2(100) = 1350 - 120 = 1230 acres left to mow.

To find the number of hours it takes to mow all the lawns, we can set ŷ = 0 and solve for x. When ŷ = 0, the equation becomes 0 = 1350 - 1.2x. Solving for x, we have 1.2x = 1350, and dividing both sides by 1.2 gives x = 1125. It takes approximately 1125 hours to mow all the lawns.