# Discounted price related math problem

#### Sirkal

You go shopping and buy a gift for a friend, but on the day before youre going to give it to him, you notice that he already has exactly what you bought him! You take the gift back to the mall, but you lost your receipt. The cashier says that you can only get back cash for the lowest amount that the item sold for. The item was originally \$50 and sales tax in your area is 9.5%. it went on sale on four different occasions. Keep in mind that when an item goes on sale, it is taxed first and then the discount is taken. The first sale was 10% off. The second sale was no tax. The third sale was buy 3, get 1 half off. The last one was buy anything over \$40 and get a $5 gift card. How much cash will you get back? #### skeeter ##### Well-known member MHB Math Helper You go shopping and buy a gift for a friend, but on the day before youre going to give it to him, you notice that he already has exactly what you bought him! You take the gift back to the mall, but you lost your receipt. The cashier says that you can only get back cash for the lowest amount that the item sold for. The item was originally \$50 and sales tax in your area is 9.5%. it went on sale on four different occasions. Keep in mind that when an item goes on sale, it is taxed first and then the discount is taken. The first sale was 10% off. The second sale was no tax. The third sale was buy 3, get 1 half off. The last one was buy anything over \$40 and get a \$5 gift card. How much cash will you get back?
Taxed first, then discount is applied? ... never have seen it work that way in actual practice, but I’ll play by the rule. So, non-discounted price including tax is $50(1.095)=54.75$ for any case.

case 1, 10% off ... $54.75(0.9)=49.28$

case 2, no tax ... you can figure this one out, I’m sure.

case 3, buy 3 get 1 half off ... $\dfrac{3.5(54.75)}{4} = 47.91$

case 4, receive a \$5 gift card for any purchase over \$40 ... you can probably figure out this one yourself, also.

#### Sirkal

##### New member
0.95 * 54 = 51.3
So that's how much I receive back from the store?

#### skeeter

##### Well-known member
MHB Math Helper
0.95 * 54 = 51.3
So that's how much I receive back from the store?
why $0.95 \cdot 54$ ? where did that come from ?

... read this part of the question again

The cashier says that you can only get back cash for the lowest amount that the item sold for.
which of the 4 cases is the lowest ?

#### Sirkal

##### New member
The second sale was no tax = 50

The last one was buy anything over \$40 and get a \$5 gift card. ---- 54.75 - 5 = 49.75