Question

If x varies directly with y and x=6 when y=8, find x when y=18.Options:13.5122412.5

Answer 1

Given:

x varies directly with y, and x=6 when y=8

Required:

We need to find the value of x when y =18.

Step-by-step explanation:

if x varies directly as y the equation of variation is expressed as follows.

`y=kx`

Substitute x =6 and y =8 in the equation to find teh value of k.

`8=k(6)`

Divide both sides by 6.

`(8)/(6)=(k(6))/(6)`
`(4)/(3)=k`

We get k =4/3.

The equation is

`y=(4)/(3)x`

Substitute y =18 in the equation to find the value of x.

`18=(4)/(3)x`

Divide both sides by 3/4.

`18*(3)/(4)=(4)/(3)x*(3)/(4)`
`13.5=x`

We get x =13.5

Final answer:

`x=13.5\text{ when y =18.}`