Difference between revisions of "2005 PMWC Problems/Problem T2"

Latest revision as of 07:13, 6 October 2007

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 $1920$ .

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

$a=8$

$b=12$

$c=20$

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

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 == Solution ==
 <math>\dfrac{abc}{2*3*5}=64=\dfrac{a^3}{8}=\dfrac{b^3}{27}=\dfrac{c^3}{125}</math>
 <math>a=8</math>
 <math>b=12</math>
 <math>c=20</math>
 <math>a+b+c=\boxed{40}</math>