Emily has a coupon for 20% off her purchase. She finds a backpack on the discount rack. It's original price is $60 but is 30% off. Emily thinks 30% & 20 % make 50% so the backpack will be $30. Is Emily correct? Explain your answer.

It is true that 20% and 30% make 50%. But in the context of sale prices it is essential to keep track of the wholes to which these percents apply. For the backpack, the 30% discount applies to the original $60 price: 30% of $60 is 0.3*60=18 making the discount on the backback $18. So after using the coupon, the backpack price becomes $42. Emily's additional 20% coupon applies not to the original backpack price but to the discounted price of $42: 20% of $42 is $8.40. Emily would need to save an additional $12 off the $42 price in order to buy the backpack for $30 so her calculations are not correct.