R varies directly as S and inversely as T. When R=43 and T=914, S=37. Find S when R=√48 and T=√75.

1962 AMC 12 Problem 13

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13.

R

varies directly as

S

and inversely as

T.

When

R=\dfrac43

and

T=\dfrac9{14},

S=\dfrac37.

Find

S

when

R=\sqrt{48}

and

T=\sqrt{75}.

28

30

40

42

60

Write the variation as

R=\frac{kS}{T}

For fixed

k,

the quantity

\frac{RT}{S}

is constant

Because

R=\frac{kS}{T},

we have

S=\frac{RT}{k}.

Hence

\begin{aligned} \frac{S_2}{S_1} &=\frac{R_2T_2}{R_1T_1}\\ &=\frac{\sqrt{48}\sqrt{75}} {(\frac{4}{3})(\frac{9}{14})}\\ &=\frac{60}{\frac{6}{7}}=70. \end{aligned}

Therefore

S_2=(\frac{3}{7})\cdot70=30.

Thus, the correct answer is B.