document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=819489>Question 819489</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 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.<BR>\n" );
document.write( "At the end of the month Sammy opened his credit card statement and noticed the following three charges:<BR>\n" );
document.write( "Game Stop: $35.28<BR>\n" );
document.write( "Payless: $55.72<BR>\n" );
document.write( "Moosejaw: $96.89<BR>\n" );
document.write( "What was the original price of each item AND what was the average dollar amount Sammy spent on each purchase?<BR>\n" );
document.write( "Using MICHIGAN sales tax! 6% <BR>\n" );
document.write( "What I already solved:<BR>\n" );
document.write( "1. Work backwards<BR>\n" );
document.write( "2. Undo the tax<BR>\n" );
document.write( "3. $55.72 - $3.15 (tax)= $52.57<BR>\n" );
document.write( "   $35.28 - $2.54 (tax)= $32.74<BR>\n" );
document.write( "   $96.89 - $5.48 (tax)= $91.41<BR>\n" );
document.write( "4. Undo the percent off<BR>\n" );
document.write( "5. Total of 45% saved at Payless<BR>\n" );
document.write( "   Total of 55% saved at Game Stop<BR>\n" );
document.write( "   Total of 35% saved at Moosejaw<BR>\n" );
document.write( "*This is the part of the process I don't understand \r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #493158 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=493158\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Sammy bought three very different items.<BR>\n" );
document.write( "I would expect that \"the average dollar amount Sammy spent on each purchase\" means the total money spent divided by 3.<BR>\n" );
document.write( "He spent money at each store, and that money included discounted price and tax, and then he spent money on gift wrapping for each of the 3 gifts. That is all the money he spent.<BR>\n" );
document.write( "The average he spend per gift would be the total money he spent divided by 3:<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2835.28%2B55.72%2B96.89%2B3%2A2.75%29%2F3 ALIGN=MIDDLE  ALT=\"%2835.28%2B55.72%2B96.89%2B3%2A2.75%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >= $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2835.28%2B55.72%2B96.89%2B8.25%29%2F3 ALIGN=MIDDLE  ALT=\"%2835.28%2B55.72%2B96.89%2B8.25%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >= $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=196.14%2F3 ALIGN=MIDDLE  ALT=\"196.14%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >= $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2865.38%29 ALIGN=MIDDLE  ALT=\"highlight%2865.38%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "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.<BR>\n" );
document.write( "I do not know why you were trying to go through complicated steps labeled 1. through 5.<BR>\n" );
document.write( "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.<BR>\n" );
document.write( " <BR>\n" );
document.write( "EXTRA:<BR>\n" );
document.write( "On another note, I cannot figure out how you calculate the undoing of the tax.<BR>\n" );
document.write( "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.<BR>\n" );
document.write( "I would calculate price easily with one division. Calculatin the tax would be harder.<BR>\n" );
document.write( "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:<BR>\n" );
document.write( "$35.28 ÷ 1.06 = $33.28 (rounded)<BR>\n" );
document.write( "$55.72 ÷ 1.06 = $52.57 (rounded)<BR>\n" );
document.write( "$96.89 ÷ 1.06 = $94.41 (rounded)<BR>\n" );
document.write( "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<BR>\n" );
document.write( "Tax on game = $<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=35.28%2A0.06%2F1.06 ALIGN=MIDDLE  ALT=\"35.28%2A0.06%2F1.06\"   DISABLED_style= \"max-width:90%; height:auto;\" >= $2.00 (rounded)<BR>\n" );
document.write( " <BR>\n" );
document.write( "Also, if you wanted to find the list price before the discount, you would do it similarly.<BR>\n" );
document.write( "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.<BR>\n" );
document.write( "To \"undo the discount you would divide by 0.45.<BR>\n" );
document.write( "So the original price of the game Sammy paid $33.28 plus tax for would have been<BR>\n" );
document.write( "$33.28 ÷ 0.45 = $73.96.<BR>\n" );
document.write( "However, Sammy saved less than that, and the original price was not that high.<BR>\n" );
document.write( "There was an original price, and the Game Stop store reduced it by 35% to<BR>\n" );
document.write( "100% - 35% = 65% of the original price.<BR>\n" );
document.write( "That would be 0.65 times the original price.<BR>\n" );
document.write( "Then, Sammy used his special pass to take an additional 20% off that final price to get it down to<BR>\n" );
document.write( "100% - 20% = 80% of the already discounted price the store was giving to people without the pass.<BR>\n" );
document.write( "That meant with the pass Sammy paid 0.80 times the price people would pay without the pass.<BR>\n" );
document.write( "The final price Sammy paid was the original (undiscounted) price times 0.65 and them multiplied times 0.8. That is the same as multiplying times<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0.65%2A0.8=0.52 ALIGN=MIDDLE  ALT=\"0.65%2A0.8=0.52\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so Sammy paid 52% of the original price, saving<BR>\n" );
document.write( "100% - 52% = 48% , not 35% + 20% = 55%.<BR>\n" );
document.write( "That is because the 20% final discount is calculated on the smaller sale price Game Stop was asking from customer without the extra discount pass.<BR>\n" );
document.write( "So the original price must have been<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3328%2F0.52 ALIGN=MIDDLE  ALT=\"3328%2F0.52\"   DISABLED_style= \"max-width:90%; height:auto;\" >= $64<BR>\n" );
document.write( "The 35% off sale at Game Stop reduced that price by<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2A0.35 ALIGN=MIDDLE  ALT=\"64%2A0.35\"   DISABLED_style= \"max-width:90%; height:auto;\" >=$22.40 to $64 - $22.40 = $41.60<BR>\n" );
document.write( "which is 65% of the original price :<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64%2A0.65 ALIGN=MIDDLE  ALT=\"64%2A0.65\"   DISABLED_style= \"max-width:90%; height:auto;\" >= $41.60.<BR>\n" );
document.write( "On that discounted \"final\" price they applied the extra 20% discount from Sammy's pass to reduce that price further by<BR>\n" );
document.write( "${41.60*0.2}}}= $8.32 to $41.60 - $8.32 = $33.28<BR>\n" );
document.write( "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 $41.60,<BR>\n" );
document.write( "$<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=41.6%2A0.8 ALIGN=MIDDLE  ALT=\"41.6%2A0.8\"   DISABLED_style= \"max-width:90%; height:auto;\" >= $33.28,<BR>\n" );
document.write( "which is really 52% of $64. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );