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 

<pre>
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:
{{{.5512/1 = 35.28/V}}}
.5512V = 35.28 ------ Cross-multiplying
V, or original price of video = {{{35.28/.5512}}}, or 64.00580552 &#8776; ${{{highlight_green(64.01)}}}

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:
{{{.636/1 = 55.72/S}}}
.636S = 55.72 ------ Cross-multiplying
S, or original price of shoes = {{{55.72/.636}}}, or ${{{highlight_green(87.61)}}}

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:
{{{.7208/1 = 96.89/P}}}
.7208P = 96.89 ------ Cross-multiplying
P, or original price of pullover = {{{96.89/.7208}}}, or ${{{highlight_green(134.42)}}}

As the wrapping wasn't done at any of the 3 stores, the purchases remain the same.

Average dollar amount spent: {{{(35.28 + 55.72 + 96.89 + 3(2.75))/3}}}, or ${{{(187.89 + 8.25)/3}}}, or {{{196.14/3}}}, or ${{{highlight_green(65.38)}}}
You can do the check!! 

Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.
Further help is available, online or in-person,for a fee, obviously. 

For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams, 
GENERAL MATH QUESTIONS, MATH HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra,
Regents Geometry, Regents Algebra 2/Trigonometry, SHSAT, COOP/HSPT/TACHS, PSAT, SAT, ACT, SSAT/ISEE, GRE, CLEP,
and the GED, you can visit: http://asvabstudyzone.freeforums.net/.