Math: Solving For x?

Question

Ok, one is selling a service and charges $30 per hour. A new platform to sell the service will charge 20%. One would want to charge more to cover the 20% cost to maintain $30 per hour at the end of the transaction.

My non-mathematical mind says this: x - 20% = $30 (solve for x)

No deal because that equation comes out to $30.20. Reversing it $30.20 - 20% = 24.16. Obviously, $24.16 is not $30

Where did I go wrong?

Answer 1

Let P = Service Price that results in a $30 profit.

P less 20% of P is equal to $30.

P - .2P = 30

.8P = 30

P = 30/.8 Dividing both sides of the equation by .8

P = $ 37.50

Charge $ 37.50 for your service, and 20% of $ 37.50($ 7.50) is used for the new platform.

CHECKING:

$ 37.50 - 20% OF $ 37.50 = $ 37.50 - $ 7.50 = $30.00

Hope this is helpful MICHAEL.

BTW, your statement of x - 20% = $30 (solve for x) just omitted one thing.

You are subtracting 20% of X. i.e. X - .2X = 30