Question

If x varies inversely as y and directly as t, and x = 12 when t = 10 and y = 25, find y when x is 6 and t = 3. 9 3/5 15 166 2/3

Answer 1

answer : 15

x varies inversely as y and directly as t

We use formula $x = \frac{kt}{y}$

x varies inversely as y so we divide by y

x varies directly as t so we multiply x

k is the constant of proportionality

Lets find out k using the given values

x = 12 when t = 10 and y = 25

$x = \frac{kt}{y}$

$12 = \frac{k*10}{25}$

Multiply by 25 on both sides

300 = 10k (divide by 10)

So k = 30

Lets find y when x is 6 and t = 3. we got k = 30

$6 = \frac{30*3}{y}$ (cross multiply)

6y = 90 (divide by 6 )

$y = \frac{90}{6} =15$

The value of y = 15