Hi, I need some help with this percent math problem...?

Question

Sweaters already on sale for 40% off the regular price cost $36 when purchased with a promotional coupon that allows an additional 20% discount. Find the original price. (Hint: When you save 40%, you are paying 60%.) I don't know how to set it up properly so it would be great if you could help, thanks!

Answer 1

Let p = the original price of a sweater

40% of the regular price is taken off of the regular price when a sweater is on sale:

40% of the price = 0.40p

Since a sweater on sale costs 40% less than the original price, the resulting expression is p - 0.40p.

With the additional 20% discount, 20% of the regular price is deducted:

20% of the price = 0.20p

and the resulting expression is

p - 0.40p - 0.20p.

With the 40% and 20% discount, a sweater now costs $36.  So, set the above expression equal to 36:

p - 0.40p - 0.20p = 36.  Solve for p.  Subtract like terms:

0.40p = 36.  Divide both sides by 0.40:

p = 90

The original price of a sweater is $90.

Hope that helped!