Algebra word problem

Question

A farmer has 1,130 acres of land on which he grows corn, wheat, and soybeans. It costs $45 per acre to grow corn, $60 to grow wheat, and $50 to grow soybeans. Because of market demand the farmer will grow twice as many acres of wheat as of corn. He has allocated $59,800 for the cost of growing his crops. How many acres of each crop should he plant?

Answer 1

Because you have 3 unknowns (acreage for corn, wheat, & soybeans), you must have at least 3 equations!

Start with what you are given...

You know that the TOTAL acreage is 1,130. So your first equation might be the sum of all 3 types: C+W+S=1130.

You also know the TOTAL $$ set aside for producing such crops and how much EACH type costs to grow. So you can set up a cost equation: 45C+60W+50S=59,800.

Can you use other information to come up with a third equation?

Then use matrices or elimination/substitution to solve for each variable.

I hope this helps! Please let me know if you need further assistance!