Question

z varies directly as x and inversely as y? If z = 51 when x = 36 and y = 3, find z if x = 25 and y = 7. (Round off your answer tothe nearest hundredth.)

Answer 1

ANSWER

15.18

EXPLANATION

If z varies directly as x, then the relationship between them is,

$z=kx$

But z also varies directly has y, so the relationship between z and these two variables is,

$z=k\cdot\frac{x}{y}$

We have to find k, knowing that z = 51 when x = 36 and y = 3,

$\begin{gathered} 51=k\cdot\frac{36}{3} \\ \\ 51=k\cdot12 \end{gathered}$

Solving for k,

$k=\frac{51}{12}=\frac{17}{4}$

Thus, the relationship is,

$z=\frac{17}{4}\cdot\frac{x}{y}$

Now, if x = 25 and y = 7, then z is,

$z=\frac{17}{4}\cdot\frac{25}{7}=\frac{425}{28}\approx15.18$

Hence, the value of z when x = 25 and y = 7 is 15.18, rounded to the nearest hundredth.