Question 1139505
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It COULD be a system of equations problem; as such, it would be a good exercise in solving such problems.<br>
However, it is much easier to solve if you write and solve a single equation using a single variable.<br>
It will take a little extra time to figure out how to write the single equation in a single variable; but solving that single equation will take far less time than solving a system of three equations in three variables.<br>
Here is how you would probably set up the problem using three variables....<br>
Let x = acres of soybeans
Let y = acres of corn
Let z = acres of wheat<br>
Then<br>
(1) x+y+z = 500  (the total acreage is 500)
(2) y = 2x  (twice as many acres of corn as soybeans)
(3) 120x + 100y + 80z = 51000  (his profit is $51,000)<br>
You would probably replace "y" with "2x" in (1) and (3) and then use elimination to solve for either x or z, and then proceed from there....<br>
Here is how you could set up the equation using a single variable:<br>
Let x = acres of soybeans
Then 2x = acres of corn  (twice as many acres of corn as soybeans)
And (500-3x) = acres of wheat  (the total acreage is 500; 3x of that is corn or soybeans)<br>
Then the single equation is<br>
{{{120(x)+100(2x)+80(500-3x) = 51000}}}
{{{120x+200x+40000-240x = 51000}}}
{{{80x = 11000}}}
{{{x = 137.5}}}<br>
ANSWER: x=137.5 acres of soybeans; 2x = 275 acres of corn; (500-412.5) = 87.5 acres of wheat