# NEW SUMMER CLOTHES

Date of the Problem
April 24, 2023

Nona went shopping to buy some new summer clothes. At the first store, she bought two pairs of pants, each originally priced \$30. Nona used a coupon that reduced the price of each item by 15%, and then a 5% sales tax was applied to the new subtotal. What was the total purchase price?

A 15% discount means that the sale price of each pair of pants was 85% of the original price, or (0.85)(30) = \$25.50, making the new subtotal 25.50 × 2 = \$51.00. Applying a 5% sales tax means the total purchase price is 105% of this subtotal, or (1.05)(51) = \$53.55.

At the next store, Nona bought a \$50 dress and used two coupons, one for 20% off and one for 10% off. How much more would Nona have saved by using a single coupon for 30% off compared to using the 20% coupon and the 10% coupon?

The sale price of an item discounted 20% would be 80% of the original price. The sale price of an item discounted 10% would be 90% of the original price. Applying the 20% coupon and the 10% coupon results in a sale price that is 0.90 × 0.80 = 0.72 = 72% of the original price. The sale price of an item discounted 30% would be 70% of the original price. Applying a single 30% coupon results in a sale price that is 70% of the original price. Therefore, by using a single 30% coupon, Nona would have saved an additional 72 − 70 = 2%, or (0.02)(50) = \$1.00, compared to using the 20% coupon and the 10% coupon.

After making a few more stops and a few more purchases, Nona went home. After putting away her new purchases, Nona noticed that she had 9 pairs of pants, 12 shirts and 3 belts. How many possible outfits can Nona make, each consisting of a pair of pants and a shirt and that may, or may not, include a belt?

There are (9)(12) = 108 combinations consisting of a pair of pants and a shirt. There are 3 belts but an outfit may, or may not, include a belt, thus there are 4 options. Therefore, the total number of possible outfits Nona can make with the clothes in her closet is 108(4) = 432 outfits.

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Page 2 contains ONLY PROBLEMS. ♦

Math topic
CCSS (Common Core State Standard)
Difficulty