Carlos pays for dinner with a friend. he uses a coupon for $5 off the price of dinner, before taxes are applied. the tax rate is 8%. the total cost for dinner after the coupon and taxes is $30.78. what is the original price of dinner before the coupon and taxes.

Now after the coupon of $5.00 and after paying the taxes at the rate of 8%. He paid $30.78 for the dinner.

So, lets say the actual price of the dinner was 'x' dollars.

Now, 8% of x dollars can be written as,

, this is the amount he needs to pay in addition to the original price (since it is taxation on the actual price).

And he got off of $5.00 from the coupon.

So after all the deductions and payment of tax, he paid $30.78, which can also be written as:

Solving for 'x' we get:

Therefore, the actual cost of the dinner is $33.13.