Jeremy is organizing his CD collection. He has 16 rock CDs, 12 rap CDs, and 20 classical CDs. If he wants to group the CDs so that each group contains the same number of rock, rap, and classical, what is the greatest number of groups that he could make?

(with explanation)

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

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