\[ \large \begin{cases}{ \color{blue}a \times \color{brown}b \times \color{green}c = \color{violet}{15}} \\ {\color{brown}b \times \color{green}c\times \color{red}d = \color{violet}{30}} \\ {\color{green}c\times \color{red}d \times \color{blue}a = \color{violet}{10}} \\ {\color{red}d \times \color{blue}a \times \color{brown}b = \color{violet}{6}}\end{cases} \]
Given \(a, b, c,\) and \(d\) are four distinct natural numbers that satisfy the system of equations above.
Determine the value of \(a+b+c+d\).
+538 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.
