Question 819639
ORIGINAL PRICE ON EACH ITEM:
The game at Game Stop was originally priced at $64.00.
For the sale, the store reduced the price by 35%, so the reduced price ended up being
100% - 35% = 65% of the original price
${{{64.00*0.65}}}= ${{{41.60}}} .
The extra 20% from Sammy's pass reduced the price further by 20% calculated based on the $41.60 sale price.
That is a reduction of
${{{41.60*0.20}}}= ${{{8.32}}}
So Sammy ended up paying $41.60 - $8.32 = $33.28 (plus tax).
That $33.28 can be calculate directly as 80% of $41.60:
${{{41.60*0.8}}}= ${{{33.28}}}
That twice reduced price is not 55% less than $64.00.
You cannot add percentages that are not applied to the same (original price.
Finally, the tax was calculated based on the final $33.28 price, and that increased the amount paid for the game by
${{{33.28*0.06}}}= ${{{2.00}}} (rounded) for a total paid of
$33.28 + $2.00 = $35.28, which is
100% + 6% = 106% of the final price,
which can be calculated directly by multiplying the final price by {{{1.06}}}
So, with all those percentages the original price was multiplied by {{{0.65}}}, then by {{{0.8}}}, and finally by {{{1.06}}} to get the final billed amount.
If rounding errors from each step did not add up, the result would be the same  as multiplying times
{{{0.65*0.8*1.06=0.5512}}},
which means that we could undo all the multiplications by dividing by 0.5512:
$35.28 ÷ 0.5512 = $64.01 (rounded)

For the shoes at payless the original price was reduced by 25%, to
100% - 25% = 75% of the original price.
That means that the original price was multiplied times {{{0.75}}} to get the sale price.
Sammy's pass meant that the sale price was reduced by a further 20% to
100% - 20% = 80% of the already reduced sale price.
That means that the sale price was multiplied times {{{0.80}}} to get Sammy's final price.
Then 6% sales tax was added, increasing the amount Sammy paid to
100% +65 = 106% of the final special price Sammy got.
That means Sammy's special price was multiplied times {{{1.06}}}.
To undo all those calculations, we can divide, first by {{{1.06}}} to undo the tax, then by {{{0.80}}} to undo the special 20% discount, and finally by {{{0.75}}} to undo the sale price reduction.
We could even round at each step.
We can undo it all at once by dividing by
{{{0.75*0.8*1.06=0.636}}}
It should give the same result, or almost the same if roundings add up.
$55.72 ÷ 0.636 = $87.61
 
For the pullover bought at Moosejaw, the factor for the one-day sale 15% price reduction applied first is {{{0.85}}} , and after that the same {{{0.80}}} and {{{1.06}}} factors were applied to calculate Sammy's special discount and the price plus tax respectively.
The overall factor is
{{{0.85*0.80*1.06=0.7208}}} and the original price was
$96.89 ÷ 0.7208 = $134.42