SOLUTION: 1. An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price

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Question 252905: 1. An instrument store gives a 10% discount to all students off the original cost of an instrument. During a back to school sale an additional 15% is taken off the discounted price. Julie, a student at the local high school, purchases a flute for $306. How much did it originally cost?

Found 2 solutions by Theo, richwmiller:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
x = retail price.

x - .10*x = discount price to all students.

this is the same as discount price to all students is .9*x

.9*x - .15*(.9*x) = price with additional discount for back to school sale.

this simplifies to be price with additional discount for back to school sale to all students = .9x - .135*x = .765*x.

total discount = .765*x.

.765*x is what she bought the flute for.

Since she paid $306.00, then:

.765*x = $306.00

divide both sides of this equation by .765 to get:

x = 306/.765 = $400.

The original retail price for the flute was $400.

10% discount off of $400 = $400 - $40 = $360.

15% additional discount off of $360 = $360 - $54 = $306.00

answer is confirmed as correct.

answer is original retail price of the flute is $400.00


Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
Since she got 10% off she paid 90%
Since she got 15% off she paid 85%
Notice that contrary to some myths it makes no difference which percent is taken first but she does get less than 25%
You can't just add the 10 and 25 to get 25%
If they were specific dollars amounts it does matter which is first
From a math standpoint, why doesn't the order matter?
What is the property about order of multiplication (and addition) ?
Commutative - Surely you remember that! -lol
.85(.90x)=306
x=400 dollars
first she got 10%=40
which brought it down to 360
then 15% more= 54 more
85% *360=306
.85*.90=.765
She paid 76.5 percent not 75 %