Question

The area is (2x + 15) square centimeters.

The ratio of the shaded region to the unshaded region is 3 : 2.
Write an algebraic expression for the area of the shaded region in terms of x.

Answer 1

`Area\:shaded=(3)/(5) (2x+15)`

Explanation:

Let
`s` be the shaded area and
`u` be the unshaded area, then we know that

(1).
`(s)/(u)=(3)/(2)`

and

(2).
`s+u=(2x+15)`

We solve for
`u` in the first equation and get:

`u=(2)/(3)s`

and put this into the second equation and get:

`s+(2)/(3)s=(2x+15)`

`s(1+(2)/(3) )=(2x+15)`

`s((5)/(3) )=(2x+15)`

`\boxed{s=(3)/(5) (2x+15)}`