Question

John owns a lawn mowing and landscaping business. The income from the business is given by the function f(x) = 2x + 54, where f(x) is the income in dollars and x is the area in square meters of lawn mowed. If John has earned {204, 344, 450, 482} dollars in the last four months, what are the corresponding areas of lawn he mowed?

A.
{75, 145, 198, 214}
B.
{84, 123, 204, 254}
C.
{70, 135, 184, 195}
D.
{80, 110, 185, 246}
E.
{95, 148, 175, 206}

Answer 1

A. {75, 145, 198, 214}

Step-by-step explanation

From the given information,the income is given by the function

`f(x) = 2x + 54`

where f(x) is the income in dollars and x is the area in square meters of lawn mowed.

To find the area that corresponds to John's earnings, we equate the function to the earnings and solve for x.

For the area that corresponds to 204, we have

`2x + 54 = 204`

`2x = 204 - 54`

`2x = 150`

`x = 75`

For the area that corresponds to 344, we have:

`2x + 54 = 344`

`2x = 344 - 54`

`2x=290`

`x = 145`

For the area that corresponds to 450, we have

`2x + 54 = 450`

`2x= 450 - 54`

`2x =396`

`x = 198`

For the area that corresponds to 482, we have

`2x + 54 = 482`

`2x= 482 - 54`

`2x = 428`

`x = 214`

Therefore the correct answer is A.