1954 AHSME Problems/Problem 3

Problem 3

If $x$ varies as the cube of $y$ , and $y$ varies as the fifth root of $z$ , then $x$ varies as the nth power of $z$ , where n is:

$\textbf{(A)}\ \frac{1}{15} \qquad\textbf{(B)}\ \frac{5}{3} \qquad\textbf{(C)}\ \frac{3}{5} \qquad\textbf{(D)}\ 15\qquad\textbf{(E)}\ 8$

$x=k\cdot y^3$ , $y=j\cdot z^{\frac{1}{5}}\implies y^3=j^3\cdot z^{\frac{3}{5}}$ , so $x=k\cdot j^3\cdot z^{\frac{3}{5}}$ , $\fbox{C}$

1954 AHSC (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
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