Farmer Brown planted corn and wheat on his 460 acres of land

Question

 The cost of planting and harvesting corn (which includes seed, planting, fertilizer, machinery, labor, and other costs) is $ 280 per acre. The cost of planting and harvesting wheat is $ 135 per acre. If Farmer Brown's total cost was $ 104,150, how many more acres of corn than wheat did the farmer plant?

Answer 1

Let x=acres of corn

     y=acres of wheat

We have 2 unknowns, so we need 2 equations to solve them:

     x+y=460

    280x+135y=104,150

Let's use the substitution method. Using the first equation and solving for "x"  we get:

    x=460-y

Using this value for "x", solve for "y" in the second equation:

    280x+135y=104,150

    280(460-y)+135y=104,150

    128,800-280y+135y=104,150

    -280y+135y=104,150-128,800

    -145y=-24,650

          y=-24,650/-145

          y=170

Using this value for "y" in the first equation we can solve for "x":

         x+y=460

         x=460-y

         x=460-170

         x=290

Use these values for "x" and "y" in the second equation to make sure the values are good:

        280x+135y=104,150

        280(290)+135(170)=104,150

        81,200+22,950=104,150

        104,150=104,150   check

Therefore, there is 290 acres of corn and 170 acres of wheat. This means that there is more acres of corn planted than acres of wheat by the equation x-y=290-170=120. There is 120 more acres of corn planted than wheat.