SOLUTION: I have 3 numbers whose sum is 60. The middle number is four time the smallest number. What is the maximum product of the two larger number?

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Question 361779: I have 3 numbers whose sum is 60. The middle number is four time the smallest number. What is the maximum product of the two larger number?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
A%2BB%2BC=60
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.
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B=4%2AA
Substituting.
A%2B4A%2BC=60
1.5A%2BC=60
Then the product is,
P=AC
From eq. 1,
C=60-5A
Substitute,
P=A%2860-5A%29
P=60A-5A%5E2
To find the maximum, put the equation into vertex form by completing the square.
P=-5A%5E2%2B60A
P=-5%28A%5E2-12A%29
P=-5%28A%5E2-12A%2B36%29%2B5%2836%29
P=-5%28A-6%29%5E2%2B180
The maximum occurs when highlight%28A=6%29 and has a value of highlight%28P%5Bmax%5D=180%29.
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B=4A
highlight%28B=24%29
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C=60-5%286%29
highlight%28C=30%29