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\[ \large \begin{cases}{ \color{blue}a \times \color{brown}b \times \color{green}c = \color{violet}{15}} \\ {\color{brown}b \times \color{green}c\times \color{red}d = \color{violet}{30}} \\ {\color{green}c\times \color{red}d \times \color{blue}a = \color{violet}{10}} \\ {\color{red}d \times \color{blue}a \times \color{brown}b = \color{violet}{6}}\end{cases}  \]


Given \(a, b, c,\) and \(d\) are four distinct natural numbers that satisfy the system of equations above.

Determine the value of \(a+b+c+d\).

 Jan 20, 2021
 #1
avatar+536 
+1

If we multiply all of them together we get a^3*b^3*c^3*d^3=27000.

The square root of that is a*b*c*d=30.

We can independently solve for each number with the above equations.

So a=1, b=3, c=5, and d=2.

 

1+3+5+2=11.

 Jan 20, 2021
 #2
avatar
+1

 

"The square root of that is a*b*c*d=30."    Did you mean to say the cube root? 

Guest Jan 20, 2021
 #3
avatar+536 
+1

right, messed up there

MooMooooMooM  Jan 20, 2021

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