Question

If y varies directly with x, and If y = 14 when x = 5, how do you find x when y = 28?

Answer 1

10

Explanation:

`y prop x implies y = kx` where `k` is a proportionality constant.

Can do this in two ways.

`color(blue)("Method One")`

`y = kx implies k = y/x = 14/5`

`x = y/k = 28/(14/5) = 10`

`color(blue)("Method Two")`

`y_1 = kx_1 and y_2 = kx_2`

`y_2/y_1 = (kx_2)/(kx_1) = x_2/x_1`

`implies x_2 = x_1y_2/y_1`

`x_2 = 5*(28)/(14) = 10`

Although the second method seems more effort just now, if you progress in maths or especially if you do physics you'll quickly find that formulae can have a lot of variables and a quick way to figure out the effects of changing one of them is to use ratios as shown in the second method.