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# Price Problem

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Nona went shopping to buy some new school 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? 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?

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?

Olpers  Aug 26, 2018
edited by Olpers  Aug 26, 2018
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Both started at $$30$$ but then were discounted by $$15%$$%. That means that the discounted price is $$85$$% of $$30$$. Given this, we have $$30 \times 0.85 = 25.5$$, which is our price. Now, we need to add a $$5$$% tax. We can get $$25.5 \times 1.05 = 26.775 ≈ 26.78$$. Since it was asking for the total price, and Nona bought two pairs of pants, we would have $$26.78\times2 = 53.56$$.

Next, let's move onto the discounts of a dress:

We have two cases;

Case 1: A $$50$$ dollar dress that was discounted by $$20$$% and $$10$$%

Case 2: A $$50$$ dollar dress that was discounted $$30$$%

Case 1: Both the coupons added would be $$0.90(0.80(50))$$ which equals $$36$$.

Case 2: We have $$0.70 \times 50$$ which equals $$35$$.

Wow, what a close call. The $$30$$% coupon saves $$1$$ more than the $$20$$% and $$10$$% coupons.

Finally, let's see how many possible outfits Nona can make:

Nona has $$9$$ pairs of pants, $$12$$ shirts and $$3$$ belts, and an outfit can consist of a pair of pants, a shirt and a belt or no belt.

We will start with the pants and shirts. In order to find all possible combinations, we can do $$9 \times 12 = 108$$. We will save that number, and use it for our next step. In order to find the possible amount of outfits with a belt, we can do $$108 \times 3 = 324$$. So $$324$$ is the number of outfits WITH a belt, and $$108$$ is the number of outfits WITHOUT a belt. When we add these, we get our answer, $$432$$.

- Daisy

dierdurst  Aug 26, 2018