Question

If y varies inversely as x, and y=7 when x=6, what is y when x=3?

Answer 1

`y=14`

Explanation:

`y prop 1/x implies y = k/x` where k is a constant of proportionality.

`y_1 = 7, x_1 = 6`
`y_2 = ?, x_2 = 3`

`(y_2)/(y_1) = (k/x_2)/(k/x_1) = k/x_2*x_1/k = x_1/x_2`

`therefore y_2 = y_1*x_1/x_2`

`y_2 = 7*6/3 = 7*2 = 14`