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2005 PMWC Problems/Problem T2

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Problem

Compute the sum of $a$ , $b$ , and $c$ given that $\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{5}$ and the product of $a$ , $b$ , and $c$ is $1920$ .

Solution

$\dfrac{abc}{2*3*5}=64=\dfrac{a^3}{8}=\dfrac{b^3}{27}=\dfrac{c^3}{125}$

$a=8$

$b=12$

$c=20$

$a+b+c=\boxed{40}$

See also

2005 PMWC (Problems)
Preceded by Problem I14	Followed by Problem T1
I: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 T: 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10

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