SOLUTION: A grower has 50 tons of melons in a field and can sell them now at $40 a ton. For each week she waits, the crop will increase by 10 tons, while the price drops by $4 a ton. When

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A grower has 50 tons of melons in a field and can sell them now at $40 a ton. For each week she waits, the crop will increase by 10 tons, while the price drops by $4 a ton. When       Log On


   

Question 589703: A grower has 50 tons of melons in a field and can sell them now at $40 a ton. For each week she waits, the crop will increase by 10 tons, while the price drops by $4 a ton. When should she sell in order to make $2160?
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
We can write the quantity for each week, x, as:
q(x) = 50 + 10x
And the price as:
p(x) = 40 - 4x
The revenue is p*q
We need to solve for x, when p*q = 2160:
(50+10x)(40-4x) = 2160
2000 + 200x - 40x^2 = 2160
Simplify:
x^2 - 5x + 4 = 0
(x-4)(x-1) = 0
This gives x = 1, x = 4
So if she sells the 1st week or 4th week, she makes $2160