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A farmer plants soybeans, corn, and wheat and rotates the planting each year on his 500 acre farm.
In a particular year, the profits from his crops were $120 per acre of soybeans, $100 per acre of corn, and $80 per acre of wheat.
He plants twice as many acres of corn as soybeans.
How many acres did he plant with each crop the year he made a total profit of $51,000?
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This problem is to be solved using one equation in one single unknown.
Let x be the area for soybeans (in acres).
Then the area for corn is (2x) acres, and the area for wheat is the rest (500-x-2x) = (500-3x) acres.
His total profit is then
120x + 100*(2x) + 80*(500-3x) = 51000 dollars.
Simplify and solve for x
120x + 200x + 40000 - 240x = 51000
80x = 51000 - 40000
80x = 11000
x = = 137.5
ANSWER. 137.5 acres for soybeans; twice of it, 2*137.5 = 275 acres for corn, and the rest, 500 - 137.5 - 275 = 87.5 acres for wheat.
Solved, explained and completed.
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To see many other similar solved problems, look into the lesson
- Advanced word problems to solve using a single linear equation
- HOW TO algebreze and solve these problems using one equation in one unknown
- Challenging word problems to solve using a single linear equation
in this site, and learn the subject from there.
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The major lesson to learn from my post is THIS :
This problem is designed, is intended, and is expected to be solved using one equation in one single unknown.
Happy learning !
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