Your friend goes shopping with $35. she buys a sweater that is on sale for half price and uses a coupon for $5 off the sale price. she has $10.50 left. what was the original price of the sweater?

Let S = the original price of the sweater. Now, lets step through the problem...

The friend goes shopping with $35 and ends up left with $10.50. This means she spent 35 - 10.50 = 24.50 on the sweater after the sale and coupon.

Next, the sweater is on sale for 50%. This means we take S and take 50% of that. S*.50

Next, she uses a $5 off coupon. Thus, we want to subtract $5 from the price. 

Lets combine this all together!

24.50 = S*.50 - 5

Solve for S.

24.50 = S*.50 - 5
29.50 = S*.50
$59 = S

Thus, the original price of the sweater was $59.