Getting right into it, we have the following cost equations: CW = $20.00 * W + $50.00 CG = $10.00 * G + $40.00
Where CW is the total cost of planting and growing Watermelons, CG is the total cost of planting and growing Grapes, W is the area of Watermelons planted, and G is the area of Grapes planted. Now that we know our cost, we can finally find our profits. Profit is equal to the price per unit area, multiplied by the area sold, subtracted by the total cost planting and growing them, or,
Profit = Price * Area - Cost
But at this point, we still don’t know the area of each crop in our field. But we do know a couple of things to figure it out. We know the total area of our farm, found in the first part. Which we can say is,
Area = G + W And we were also only given $1590 to plant the crops. So,
$1590.00= CW+CG
I’ll help you simplify this a bit, $1590.00=$20.00*W+$50.00+$10.00*G+$ 40.00
$1590.00=$20.00*W+$10.00*G+$90.00 So now we have enough information to solve for the areas of Watermelons and Grapes in your field. Here’s some room to do that. Hint: Use either substitution, or graph the two equations to find an intersection.