SOLUTION: Sammy decided to go Christmas shopping at the mall. He had won a pass that allowed him to take an additional 20% off all final price purchases at any store, which he used for each

Question 819489: Sammy decided to go Christmas shopping at the mall. He had won a pass that allowed him to take an additional 20% off all final price purchases at any store, which he used for each purchase. First Sammy went to Game Stop to by his friend a video game. Game stop was having a 35% off store-wide sale. Then, he headed off to Payless to take advantage of their 25% off everything sale, to buy a pair of shoes. His last stop was at Moosejaw to buy a pullover, because they were having a one-day sale where everything was 15% off. As Sammy was leaving the mall, he stopped at a gift wrapping booth. They were charging $2.75(tax-included) for each gift wrapped. Sammy had all three gifts wrapped.
At the end of the month Sammy opened his credit card statement and noticed the following three charges:
Game Stop: $35.28
Payless: $55.72
Moosejaw: $96.89
What was the original price of each item AND what was the average dollar amount Sammy spent on each purchase?
Using MICHIGAN sales tax! 6%
What I already solved:
1. Work backwards
2. Undo the tax
3. $55.72 - $3.15 (tax)= $52.57
$35.28 - $2.54 (tax)= $32.74
$96.89 - $5.48 (tax)= $91.41
4. Undo the percent off
5. Total of 45% saved at Payless
Total of 55% saved at Game Stop
Total of 35% saved at Moosejaw
*This is the part of the process I don't understand

Found 2 solutions by KMST, MathTherapy:
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
Sammy bought three very different items.
I would expect that "the average dollar amount Sammy spent on each purchase" means the total money spent divided by 3.
He spent money at each store, and that money included discounted price and tax, and then he spent money on gift wrapping for each of the 3 gifts. That is all the money he spent.
The average he spend per gift would be the total money he spent divided by 3:
$= $= $= $ .

If that is not what the problem means, I have to work on my reading comprehension, or the problem was written in a confusing way, or both.
I do not know why you were trying to go through complicated steps labeled 1. through 5.
It seems to me that they tossed in all kinds of superfluous, unnecessary information to see if you could understand the problem and think through it.

EXTRA:
On another note, I cannot figure out how you calculate the undoing of the tax.
You seem to magically calculate the tax (not an easy calculation, but no work shown, which makes me suspicious) and then subtract to find the price without tax.
I would calculate price easily with one division. Calculatin the tax would be harder.
When you add 6% tax (0.06 times the price) you end up paying 106% of the price (1.06 times the price), so to calculate the (already discounted) price without the tax, I would divide by 1.06:
$35.28 � 1.06 = $33.28 (rounded)
$55.72 � 1.06 = $52.57 (rounded)
$96.89 � 1.06 = $94.41 (rounded)
To calculate the amount of tax, I would have to do the difference, or multiply the price times 0.06. I could do both in one calculation line, as in
Tax on game = $= $2.00 (rounded)

Also, if you wanted to find the list price before the discount, you would do it similarly.
A 55% price discount at Game Stop would have meant that Sammy paid 100% - 55% = 45% of the listed price. To calculate the discounted price, you would take the original listed price, and multiply times 0.45.
To "undo the discount you would divide by 0.45.
So the original price of the game Sammy paid $33.28 plus tax for would have been
$33.28 � 0.45 = $73.96.
However, Sammy saved less than that, and the original price was not that high.
There was an original price, and the Game Stop store reduced it by 35% to
100% - 35% = 65% of the original price.
That would be 0.65 times the original price.
Then, Sammy used his special pass to take an additional 20% off that final price to get it down to
100% - 20% = 80% of the already discounted price the store was giving to people without the pass.
That meant with the pass Sammy paid 0.80 times the price people would pay without the pass.
The final price Sammy paid was the original (undiscounted) price times 0.65 and them multiplied times 0.8. That is the same as multiplying times
, so Sammy paid 52% of the original price, saving
100% - 52% = 48% , not 35% + 20% = 55%.
That is because the 20% final discount is calculated on the smaller sale price Game Stop was asking from customer without the extra discount pass.
So the original price must have been
$= $64
The 35% off sale at Game Stop reduced that price by
$=$22.40 to $64 - $22.40 = $41.60
which is 65% of the original price :
$= $41.60.
On that discounted "final" price they applied the extra 20% discount from Sammy's pass to reduce that price further by
${41.60*0.2}}}= $8.32 to $41.60 - $8.32 = $33.28
The last $8.32 discount is 20% of $41.60, not 20% of the original $64 price, so you cannot add discount percentages, and the $33.28 Sammy paid was 80% of $41.60,
$= $33.28,
which is really 52% of $64.
Answer by MathTherapy(10552) (Show Source): You can put this solution on YOUR website!
Sammy decided to go Christmas shopping at the mall. He had won a pass that allowed him to take an additional 20% off all final price purchases at any store, which he used for each purchase. First Sammy went to Game Stop to by his friend a video game. Game stop was having a 35% off store-wide sale. Then, he headed off to Payless to take advantage of their 25% off everything sale, to buy a pair of shoes. His last stop was at Moosejaw to buy a pullover, because they were having a one-day sale where everything was 15% off. As Sammy was leaving the mall, he stopped at a gift wrapping booth. They were charging $2.75(tax-included) for each gift wrapped. Sammy had all three gifts wrapped.
At the end of the month Sammy opened his credit card statement and noticed the following three charges:
Game Stop: $35.28
Payless: $55.72
Moosejaw: $96.89
What was the original price of each item AND what was the average dollar amount Sammy spent on each purchase?
Using MICHIGAN sales tax! 6%
What I already solved:
1. Work backwards
2. Undo the tax
3. $55.72 - $3.15 (tax)= $52.57
$35.28 - $2.54 (tax)= $32.74
$96.89 - $5.48 (tax)= $91.41
4. Undo the percent off
5. Total of 45% saved at Payless
Total of 55% saved at Game Stop
Total of 35% saved at Moosejaw
*This is the part of the process I don't understand

Let original price of video game be V
Since there was a 35% sales discount, the video's price was marked down to 65% of the original price, or .65
Since he had an additional discount of 20%, then he only paid 80% of the marked down price, or .8(.65), or
.52, or 52% of the original price for the video.
Adding 6% sales tax, the percentage of the original price he paid was: 1.06(.52), or .5512, or 55.12%.
Since he paid a total of $35.28 for the video, tax included, then we can say that:

.5512V = 35.28 ------ Cross-multiplying
V, or original price of video = , or 64.00580552 ≈ $
Let original price of shoes be S
Since there was a 25% sales discount, the shoes' price was marked down to 75% of its original price, or .75
Since he had an additional discount of 20%, then he only paid 80% of the marked down price, or .8(.75), or
.6, or 60% of the original price for the shoes.
Adding 6% sales tax, the percentage of the original price he paid was: 1.06(.6), or .636.
Since he paid a total of $55.72 for the shoes, tax included, then we can say that:

.636S = 55.72 ------ Cross-multiplying
S, or original price of shoes = , or $
Let original price of pullover be P
Since there was a 15% sales discount, the pullover's price was marked down to 85% of its original price, or .85
Since he had an additional discount of 20%, then he only paid 80% of the marked down price, or .8(.85), or
.68, or 68% of the original price for the pullover.
Adding 6% sales tax, the percentage of the original price he paid was: 1.06(.68), or .7208.
Since he paid a total of $96.89 for the pullover, tax included, then we can say that:

.7208P = 96.89 ------ Cross-multiplying
P, or original price of pullover = , or $
As the wrapping wasn't done at any of the 3 stores, the purchases remain the same.
Average dollar amount spent: , or $, or , or $
You can do the check!!
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