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 $38 and $30/acre, respectively. Jacob Johnson has $16,600 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?

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 $38 and $30/acre, respectively. Jacob Johnson has $16,600 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? ​

Quizplus · Accepted Answer

Let x be the number of acres of corn and y be the number of acres of wheat.
From the problem statement, we know:
x + y = 500 (since he wants to use all the allotted land)
38x + 30y = 16600 (since he has $16600 available for cultivating these crops)
Solving these two equations simultaneously, we get:
x = 200 and y = 300
Therefore, he should plant 200 acres of corn and 300 acres of wheat.

The Johnson Farm Has 500 Acres of Land Allotted for Cultivating