Question 1139506: I think this is a system of equations question.
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?
Found 2 solutions by algebrahouse.com, ikleyn:
Answer by algebrahouse.com(1659)   (Show Source):
You can put this solution on YOUR website!
All I can say is...You better appreciate this! It’s going to take awhile.
s = number of soybean acres
c = number of corn acres
w = number of wheat acres
s + c + w = 500 {total acres of his farm is 500}
120s + 100c + 80w = 51,000 {price per acre times number of acres = total profit}
c = 2s {he plants twice as many acres of corn as soybeans}
-80s - 80c - 80w = -40,000 {multiplied 1st equation by-80}
120s + 100c + 80w = 51,000 {2nd equation stays the same}
-—————————————
40s + 20c = 11,000 {added the two equations, cancelling the w’s}
c = 2s {3rd equation from above}
40s + 20c = 11,000 {equation created above}
40s + 20(2s) = 11,000 {substituted 2s in for c}
40s + 40s = 11,000 {multiplied}
80s = 11,000 {added}
s = 137.5 {divided by 80}
c = 2s {equation from above}
c = 2(137.5) {substituted 137.5, in for s, into c = 2s}
c = 275 {multiplied}
s + c + w = 500 {1st equation above}
137.5 + 275 + w = 500 {substituted 137.5 in for s and 275 in for c}
w + 412.5 = 500 {combined like terms}
w = 87.5 {subtracted 412.5 from each side}
137.5 acres of soybeans, 275 acres of corn, and 87.5 acres of wheat
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Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
This problem is designed and intended for 6th - 7th grade students who, as a rule, are not familiar yet with systems of linear equations.
This problem is intended and is expected to be solved by reduction to one single equation in one unknown.
Do it as the tutor @greenestamps solved it for you under this link
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1139505.html
https://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.1139505.html
Although it is possible to solve the problem by using system of 3 equations in 3 unknowns, but it is absolutely unjustified complication.
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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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Also, you posted this problem at least 3 times to the forum, starting every time with this mantra
I think this is a system of equations question.
Please keep in mind the following.
You EITHER can solve it on your own, OR not.
You EITHER know how to do it, OR not.
Since you post the problem to the forum, it means that you CAN NOT solve it on your own and DON't KNOW how to do it.
Therefore, you better do not hypothesize on how to solve it.
We, the tutors, are the experts, and we know how to do it.
So, please, either change your introductory mantra, or do not use it at all.
By the way, the best mantra to start with is THIS : "Please help me solve this problem."
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