Algebra exercise

Question

A farmer plants 70 acres with two types of beans: green and red. Each acre of green bean fills out 27 bushels and each acre of red bean fills out 36 bushels. If the farmer fills out the double amount of green bean bushels than the red beans, how many acres of red beans did the farmer plant?

Answer 1

First let's define the variables. I'll use g for green bean acres and r for red bean bushels.

g:=green bean acres

r:=red bean acres

70 acres planted with these two types of beans becomes

70=g+r (1)

27 bushels of green beans to an acre and 36 bushels to an acre of red beans and twice as many green to red

27g=2*36r (2)

since you're looking for r then you should solve for g in (2)

g=8r/3 (3)

Replacing g in (1) from (3) gives

70=(8r/3)+r (4)

70=11r/3

r=210/11=19.09 acres of red beans