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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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Let's start with the price of the pants:

 

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

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