SOLUTION: 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 $44 and $28 per acre, respecti
Question 1122294: 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 $44 and $28 per acre, respectively. Jacob Johnson has $16,400 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? (Let x and y denote the number of acres of corn and wheat, respectively.) Answer by ikleyn(52847) (Show Source):
From the condition, you have this system of 2 equations in 2 unknowns
C + W = 500 acres (1) (C is the area for corn and W is the area for wheat)
44*C + 28*W = 16400 dollars (2) (counting dollars)
From eq(1) express W = 500-C and substitute it into eq(2). You will get
44*C + 28*(500-C) = 16400,
44*C + 28*500 - 28*C = 16400
(44-28)*C = 16400 - 28*500 ====> C = = 150.
Answer. 150 acres for corn, and the rest (500-150) = 350 acres for wheat.
Solved.
On the way, you learned on how the Substitution method works in solving system of two equations in two unknowns.
