Question

Suppose y varies directly as x, and y=26 when x=8. Find x when y=65.

Answer 1

when y=65, x=20

Explanation:

We are given:

y varies directly as x

and y=26, when x=8

We need to find x, when y = 65

y varies directly as x can be written as:

`y\:\alpha \:x\\y=kx`

Where k is constant of proportionality.

Finding k, when y=26 and x=8

`y=kx\\26=k(8)\\k=(26)/(8)\\k=3.25`

We get the value of k = 3.25

Now, we need to find value of x, when y=65 and k=3.25

`y=kx\\65=3.25(x)\\x=(65)/(3.25)\\x=20`

So, when y=65, x=20