Question

The Johnson Farm has 500 acres of land allotted for cultivating corn and wheat. The cost of cultivating corn and wheat (including seeds and labor) is $42 and $32 per acre, respectively. Jacob Johnson has $17,000 available for cultivating these crops. If he wishes to use all the allotted land and his entire budget for cultivating these two crops, how many acres of each crop should he plant? Solve by any method. Define your variables, show your equations and your answer.

Answer 1

Corn is 100 acres and for wheat 400 acres.

Explanation:

Given area of land = 500 acres

Cost of cultivating corn = $42

Cost of cultivating wheat = $32

Money available with Johnson = $17000

Let x acre used for Corn and y acre used for wheat.

Thus, 42x + 32Y = 17000 …..(1)

x + y = 500 ……………….(2)

now multiply the second equation with 32.

32x + 32y = 16000

Now subtract this from first equation.

10x = 1000

x = 100 acres

Now put x in (2).

x + y = 500

100 + y = 500

Y = 400 acres

Therefore, land needed for corn is 100 acres and for wheat 400 acres.

Answer 2

Explanation:

c - #of acres of corn

w - #of acres of wheat

Total acres, c+w =500 ⇒ c=500-w

42c+32w = 17,000

42(500-w) +32w = 17,000

21,000 - 42w+32w = 17,000

21,000 -10w = 17,000

10w = 4,000

w=400acres

c=500-400=100acres