Bro Gym charges members $10 per month plus a one time fee of $100 to sign up. Muscles R' Us Gym charges members $20 per month plus a one time fee of $50 to sign up. After how many months would the cost of the gyms be equal?

it will take 5 hours for both costs to be equal

Step-by-step explanation:

Let x represent the number of months for which the cost of the gyms be equal.

Bro Gym charges members $10 per month plus a one time fee of $100 to sign up. This means that the total amount that Bro Gym charges for x hours is

10x + 100

Muscles R' Us Gym charges members $20 per month plus a one time fee of $50 to sign up. This means that the total amount that Muscles R' Us Gym charges for x hours is

20x + 50

For both cost of the gyms to be equal,

10x + 100 = 20x + 50

20x - 10x = 100 - 50

10x = 50

x = 50/10 = 5

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.