Question

If y varies inversely as x, and y=15 when x=4, find y when x=8

Answer 1

When y varies inversely with x, we have a relation like:

`y=(k)/(x)`

where k is a constant.

If we rewrite this relationship, we get:

`k=x\cdot y`

which means that the product x*y is constant for all pairs of values (x,y) in the function.

Then, if we know that y =15 when x = 4, then we can calculate y when x = 8 as:

`\begin{gathered} (x_1,y_1)=(4,15)_{} \\ (x_2,y_2)=(8,y) \\ x_1\cdot y_1=x_2\cdot y_2 \\ 4\cdot15=8\cdot y \\ 60=8y \\ y=(60)/(8) \\ y=7.5 \end{gathered}`

Answer: y = 7.5