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1. Question
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?
Correct
Let x
represent the original price of the flute. A 10% discount means the student pays 90% of the original price (x
).10% of x
is 0.10x
Price after 10% off is x−0.10x=0.90x
The 15% discount is taken off the already discounted price, not the original price, so Julie pays 85% of the discounted price:0.85×0.90x=0.765x
Julie paid $306, so 0.765x=306
.The last step is to solve to x
:306÷0.765=400
Therefore, the original price was $400.
Incorrect