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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?

Respuesta :

calculista

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

[tex]\frac{x}{y}=\frac{5}{8}[/tex]

[tex]y=\frac{8}{5}x[/tex] -----> equation A

[tex]x=50[/tex]

substitute the value of x in equation A

[tex]y=\frac{8}{5}(50)[/tex]

[tex]y=80[/tex]

step 2

Find out the total memberships after the incentive

[tex]x+y=50+80=130[/tex]

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

[tex]\frac{x}{y}=\frac{10}{3}[/tex]

[tex]y=\frac{3}{10}x[/tex] -----> equation A

[tex]x+y=130[/tex] -----> equation B

substitute equation A in equation B and solve for x

[tex]x+\frac{3}{10}x=130[/tex]

[tex]\frac{13}{10}x=130[/tex]

[tex]x=130(10)/13\\x=100[/tex]

therefore

The number of monthly memberships before the incentive was 100