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 $30 per acre, respectively. Jacob Johnson has $19,800 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.)

Question

Business

Peters

4 October, 16:57

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 $30 per acre, respectively. Jacob Johnson has $19,800 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.)

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Answers (1)

Know the Answer?

Madeleine Rivera · Answer 1

The answer is: Jacob Johnson should cultivate 400 acres of corn and 100 acres of wheat.

Explanation:

x = corn acre; y = wheat acre

Step 1:

x + y = 500

42x + 30y = 19,800

Step 2:

Multiply (x + y = 500) times - 30; - 30x - 30y = - 15,000

Step 3:

42x + 30y = 19,800

-30x - 30y = - 15,000

Step 4:

(42x - 30x) + (30y - 30y) = 19,800 - 15,000; 12x = 4,800

Step 5:

x = 4,800/12; x = 400

Step 6:

400 + y = 500; y = 100