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

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?

i know its absurdly simple but my brain feels like mush right now

Answer 1

100%-15%= 85% 306/85%= 360

100%-10%= 90% 360/90%= 400

Hope this helps

Answer 2

Do it step wise as the reverse of the original purchase.

So to get back to the discounted price (after the 10%) then multiply the £306 by 1/0.85. Then to get to the original price multiply this result by 1/0.9.

Answer 3

To find out the original cost of the flute, we can work backwards from the final price using the given information.

Let's start with the discounted price that Julie paid for the flute after applying both the student discount and the back-to-school sale discount.

First, we calculate the price after the student discount by subtracting 10% from the original cost:
Discounted price after student discount = Original cost - (10% of Original cost)
Discounted price after student discount = Original cost - (0.1 * Original cost)
Discounted price after student discount = Original cost - 0.1 * Original cost
Discounted price after student discount = Original cost - 0.1 * Original cost
Discounted price after student discount = 0.9 * Original cost

Next, we calculate the price after the back-to-school sale discount by subtracting 15% from the discounted price:
Discounted price after back-to-school sale discount = Discounted price after student discount - (15% of Discounted price after student discount)
Discounted price after back-to-school sale discount = 0.9 * Original cost - (15% of 0.9 * Original cost)
Discounted price after back-to-school sale discount = 0.9 * Original cost - (0.15 * 0.9 * Original cost)
Discounted price after back-to-school sale discount = 0.9 * Original cost - 0.135 * Original cost
Discounted price after back-to-school sale discount = (0.9 - 0.135) * Original cost
Discounted price after back-to-school sale discount = 0.765 * Original cost

We know that Julie paid $306 for the flute, so we can set up the equation:
0.765 * Original cost = $306

Now, we can solve for the Original cost:
Original cost = $306 / 0.765
Original cost ≈ $400

Therefore, the flute originally cost approximately $400.