Question

A community pool offers two types of memeberships: monthly and annual memberships. At the beginning of the year, the ratio of monthly to annual memeberships was 10:3. However, the pool offered an incentive to have members move to the annual memebership. After the incentive, the ratio was 5:8. If there were 50 monthly members after the incentive then how many monthly members were there before?

Answer 1

The number of monthly memberships before the incentive was 100

Explanation:

Remember that

The total memberships after the incentive is equal to the total memberships before the incentive

step 1

Find out the annual memberships after the incentive

Let

x -----> monthly memberships after the incentive

y -----> annual memberships after the incentive

we know that

`(x)/(y)=(5)/(8)`

`y=(8)/(5)x` -----> equation A

`x=50`

substitute the value of x in equation A

`y=(8)/(5)(50)`

`y=80`

step 2

Find out the total memberships after the incentive

`x+y=50+80=130`

step 3

Find out the monthly members before the incentive

Let

x -----> monthly memberships before the incentive

y -----> annual memberships before the incentive

we know that

`(x)/(y)=(10)/(3)`

`y=(3)/(10)x` -----> equation A

`x+y=130` -----> equation B

substitute equation A in equation B and solve for x

`x+(3)/(10)x=130`

`(13)/(10)x=130`

`x=130(10)/13\\x=100`

therefore

The number of monthly memberships before the incentive was 100