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

Answer:

The number of monthly memberships before the incentive was 100

Step-by-step 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

$\frac{x}{y}=\frac{5}{8}$

$y=\frac{8}{5}x$ -----> equation A

$x=50$

substitute the value of x in equation A

$y=\frac{8}{5}(50)$

$y=80$

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

$\frac{x}{y}=\frac{10}{3}$

$y=\frac{3}{10}x$ -----> equation A

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

substitute equation A in equation B and solve for x

$x+\frac{3}{10}x=130$

$\frac{13}{10}x=130$

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

therefore

The number of monthly memberships before the incentive was 100