Question 1201581: Your work in the tool department of Spark. A customer comes to you with a special coupon for a 10% discount the store is already running as 30% off sale. The item the customer has in hand is priced at $200. She claims that she is entitled to 40% discount. Your manager says that the 10% discount is taken off the final price after the initial 30% is deducted. Are the final prices the same? Use calculations to support your answer.
Found 2 solutions by Glaviolette, MathTherapy:
Answer by Glaviolette(140)   (Show Source):
You can put this solution on YOUR website! They are not the same. If 30% is taken off, 70% of the price remains which is $210. The coupon is then applied, leaving 90% of the sale price to pay which is $189. The additional 10% is taken off of a smaller value that the original price. If a total of 40% is taken off, 60% remains, which is $180. That is not the same as $189.
Answer by MathTherapy(10551)  (Show Source):
You can put this solution on YOUR website!
Your work in the tool department of Spark. A customer comes to you with a special coupon for a 10% discount the store is already running as 30% off sale. The item the customer has in hand is priced at $200. She claims that she is entitled to 40% discount. Your manager says that the 10% discount is taken off the final price after the initial 30% is deducted. Are the final prices the same? Use calculations to support your answer.
They're NOT the same!
Discount of 30% means that the item is sold for 70% of its original price.
An additional discount of 10% means that the item is sold for 90% of its already-reduced/discounted 70% of its original
price, or 70% times 90%, or .7(.9) = .63, or 63%. Having being discounted to 63% (.63) of its original price means that
the discount after the 2 markdowns was 37% (100% - 63%), or .37 (1 - .63).
It's quite obvious that a total discount of 37% (.37) is NOT the same as a 40% (.4) discount.
The $200 item, at a discount of 37% (.37) = (1 - .37)(200) = .63(200) = $126 FINAL PRICE.
The $200 item, at an incorrect discount of 40% (30% + 10%, or .3 + .1) = (1 - .4)(200) = .6(200) = $120 FINAL PRICE.
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