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smc

prealgebra intermediate

Problem

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:

(A)

1/15

(B)

5/3

(C)

3/5

(D)

15

Solution

x = k \cdot y^{3}

,

y = j \cdot z^{\frac{1}{5}} ⟹ y^{3} = j^{3} \cdot z^{\frac{3}{5}}

, so

x = k \cdot j^{3} \cdot z^{\frac{3}{5}}

,

\frac{3}{5}

Final answer

C