Question

17. To ensure a growing season of sufficient length, Mr. Brown has at most 16 days left to plant his corn and potato crops. He can plant corn at the rate of 250 acres per day and potatoes at a rate of 200 acres per day. He has at most 3500 acres available. Which of the following ordered pairs are a possible number of days Mr. Brown can plant corn and potatoes? Let x = the number of days corn will be planted and y = the number of days potatoes will be planted. (A. (0, 17) B. (10, 12) C. (7,8) D. (16,0)

Answer 1

we have that

`x+y\leq16`
`250x+200y\leq3,500`

using a graphing tool

the solution is the shaded area with vertices (0,0) (0,16) (6,10) and (14,0)

therefore

Verify each ordered pair

A(0,17) ------> not lie in the shaded region

B(10,12) -----> not lie in the shaded region

C(7,8) -----> lie in the shaded region

D(16,0) ----> not lie in the shaded region

therefore

the answer is C