
Anthony J. answered 11/02/18
Michigan Certified Math Teacher/tutor
Here is a special formula designed to answer any and all questions with respect to mark-up and mark-down problems. The formula is:
R (+/-) R% = New amount, Sale cost, Current amount, etc.
R = original amount
+/- = appropriate sign given the problem is a mark-up, or mark-down problem.
New amount = Sale cost, current amount, total amount, etc.
In the problem given, we are being asked to solve for the original price, therefore we are solving for R.
The sign we are going to use is (-) for it is a discount which implies subtraction...i.e., money off the original amount. Next we have the percentage off where we need to change the percentage to a decimal number. Finally, the amount of $240 is the sale price.
OUr equation becomes: R - .40R = 240. Now the trick part is solving for R. In order to solve for R, you must combine the like terms of R - .40R, then divide both sides by the resulting coefficient of R, in this case .60R.
Hope this helps.