A community pool office two types of memberships monthly and annual memberships. At the beginning of the year the ratio of monthly annual memberships is 10 to 3. However the pool offered an incentive to have members move the annual membership. After the incentive the ratio is 5 to 8. If there are 50 monthly members after the incentive and how many monthly members were there before?

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

> equation A

substitute the value of x in equation A

step 2

Find out the total memberships after the incentive

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

> equation A

> equation B

substitute equation A in equation B and solve for x

therefore

The number of monthly memberships before the incentive was 100

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

eventually after a few more steps, your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15