Formulate but do not solve the problem. 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 $28 per acre, respectively. Jacob Johnson has $16,800 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

Jayson

Mathematics

25 May, 23:54

Formulate but do not solve the problem. 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 $28 per acre, respectively. Jacob Johnson has $16,800 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)

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Victoria · Answer 1

x + y = 500

42x + 28y = 16800

Step-by-step explanation:

The total area of the land is 500 acres. The cost for cultivating corn is $42 per acre and the cost for cultivating wheat is $28 per acre. The total amount available is 16,800.

Let x denote the number of acres of corn and y the number of acres of wheat.

Since we know that all of the land needs to be used, our first equation would be:

x + y = 500

We also know that the whole amount available needs to be spent, therefore our second equation would be:

42x + 28y = 16800.

Therefore, our two equations would be

x + y = 500

42x + 28y = 16800.

To know the amount of wheat and corn, we need to solve these equations.