Question

It is given that $x$ varies directly as $y$ and inversely as the square of $z$, and that $x=10$ when $y=4$ and $z=14$. If $y=16$ and $z=7$, find the value of $x$.

• A. $180$
• B. $160$
• C. $154$
• D. $140$

Answer 1

Answer: (B)

$160$

$x\alpha \frac{y}{z^2}$

$x=\frac{ky}{z^2}$ when $x=10,y=4,z=14$

$10=\frac{k\times 4}{196}$

$k=490$

$\therefore$ when $y=16,z=7$

$x=\frac{490\times 16}{49}$

$x=160$