SOLUTION: Amelia is at looking at a sweater that costs $80. The store is having a 20% off sale and there is 8% sales tax Amelia is wondering which would cost less to take the 20% off then ad

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Question 1123865: Amelia is at looking at a sweater that costs $80. The store is having a 20% off sale and there is 8% sales tax Amelia is wondering which would cost less to take the 20% off then add the 8% tax or to add on the 8% sales tax then to take the 20% off. Help Amelia figure out which would cost less.
Found 3 solutions by Theo, josmiceli, MathTherapy:
Answer by Theo(13342) About Me  (Show Source):
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the sweater is on sale for $80.00

take the discount first and then pay the sales tax equals .8 * $80 * 1.07

pay the sales tax first and then take the discount equals $80 * 1.07 * .8

i think it will wind up being the same.

breaking it down into more detail.

the price is $80.00
20% off is .2 * $80.00 = $16.00
$80.00 - $16.00 = $64 sale price
7% sales tax on $64 = $4.48.
$64 + $4.48 = $68.48 total

the price is $80.00
7% sales tax on $80 = $5.60
$80.00 + $5.60 = $85.60
20% off is .2 * $85.60 = $17.12
$85.60 - $17.12 = $68.48 total

the total price is the same.

this has to do with the commutative law of multiplication that states that a * b is the same as b * a.

20% discount is the same as multiplying the price by .8
7% sales tax is the same as multiplying the price by 1.07

.8 * $80 * 1.07 is the same as 1.07 * $80 * .8

the .8 factor is achieved in the following manner.

x - .2 * x = x * (1 - .2) = x * .8 = .8 * x

the 1.07 factor is achieved in the following manner.

x + .07 * x = x * (1 + .07) = x * 1.07 = 1.07 * x





Answer by josmiceli(19441) About Me  (Show Source):
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20% off, then 8% added on:
+80+-+.2%2A80+=+.8%2A80+
+.8%2A80+=+64+
Then
+64+%2B+.08%2A64+=+1.08%2A64+
+1.08%2A64+=+69.12+
—————————————
8% tax first, then 20% off:
+80+%2B+.08%2A80+=+86.4+
+86.4+-+.2%2A86.4+=+.8%2A86.4+
+.8%2A86.4+=+69.12+
—————————————
They are the same

Answer by MathTherapy(10557) About Me  (Show Source):
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Amelia is at looking at a sweater that costs $80. The store is having a 20% off sale and there is 8% sales tax Amelia is wondering which would cost less to take the 20% off then add the 8% tax or to add on the 8% sales tax then to take the 20% off. Help Amelia figure out which would cost less.
Either way the cost is the same: highlight_green%28%22%2469.12%22%29