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?

Question

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?
325
375
400
408
425

GPT 3.5 · Accepted Answer

Let's assume the original cost of the flute is x.
Since Julie is a student, she receives a 10% discount, so she pays 90% of the original cost, or 0.90x.
During the back to school sale, an additional 15% is taken off the discounted price, so she pays 85% of the discounted price, or 0.85(0.90x).
We can set up the following equation to solve for x:
0.85(0.90x) = 306
Multiplying both sides of the equation by 100/85 (to remove the decimals) gives us:
(0.85/1)(0.90/1)x = (306)(100/85)
Multiplying gives us:
0.765x = 360
Dividing both sides of the equation by 0.765 gives us:
x = 360/0.765
x = 470.59
The original cost of the flute was $470.59, which is closest to $475. Answer: $\boxed{400}$.