Question

A farmer plants corn and wheat on a 180-acre farm. the farmer wants to plant three times as many acres of corn as wheat. write a system of linear equations that represents this situation. use xx to represent the number of aces of corn planted and yy to represent the number of acres of wheat planted. how many acres of each crop should the farmer plant?

Answer 1

Let the number of corn acres be xx and the number of wheat acres be yy.
We are given that:
1- The total number of acres is 180, this means that:
xx + yy = 180 ..............> equation I
2- The number of corn acres is 3 times that of wheat. This means that:
xx = 3yy .........> equation II

Substitute with equation II in equation I to get the value of yy as follows:
xx + yy = 180
3yy + yy = 180
4yy = 180
yy = 45 acres

Now substitute with yy in equation II to get xx as follows:
xx = 3yy
xx = 3*45
xx = 135 acres

Based on the above calculations:
acres of corn = xx = 135 acres
acres of wheat = yy = 45 acres