Question

A farmer wants to plant peas and carrots on no more than 200 acres of his farm. If x represents the number of acres of peas and y represents the number of acres of carrots for solution (x, y), then which is a viable solution?

A.(−50, 160)
B.(80, 160)
C.(75, −200)
D.(60, 135)

Answer 1

D

Explanation:

Answer 2

Option D.(60, 135)

Explanation:

Let

x -----> the number of acres of peas

y ----> the number of acres of carrots

we know that

The inequality that represent the problem is equal to

`x+y\leq 200`

so

Verify each case

case A) (-50,160)

substitute the value of x and the value of y in the inequality and then compare the result

`-50+160\leq 200`

`110\leq 200` ----> is true

The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number

case B) (80,160)

substitute the value of x and the value of y in the inequality and then compare the result

`80+160\leq 200`

`240\leq 200` ----> is not true

therefore

The point is not a solution

case C) (75,-200)

substitute the value of x and the value of y in the inequality and then compare the result

`75-200\leq 200`

`-125\leq 200` ----> is true

The point is a solution for the inequality, but is not a viable solution because the number of acres can not be a negative number

case D) (60,135)

substitute the value of x and the value of y in the inequality and then compare the result

`60+135\leq 200`

`195\leq 200` ----> is true

therefore

The point is a viable solution