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?
let the original cost be x
(.9)(.85)x = 306
x = 306/(.9(.85)) = 400
check: 10 off $400 = 400-40= 360
15% off 360 = 360 - 54 = 306
Let's solve this step by step:
Step 1: Let's assume the original cost of the flute is X dollars.
Step 2: Julie, being a student, receives a 10% discount on the original cost of the flute. Therefore, she pays 90% of the original cost:
0.90(X) = 0.9X
Step 3: During the back-to-school sale, an additional 15% is taken off the discounted price. Therefore, the final price that Julie paid is 85% of the discounted price:
0.85(0.9X) = 0.765X
Step 4: We are given that Julie purchased the flute for $306. So we can set up the equation:
0.765X = $306
Step 5: To find the value of X (the original cost), we divide both sides of the equation by 0.765:
X = $306 / 0.765
Step 6: Calculating the value of X:
X = $400
Therefore, the flute originally cost $400.
To find the original cost of the flute, we can work backwards step by step. Let's start by assuming the original cost of the flute is X dollars.
Step 1: Applying the student discount
The instrument store gives a 10% discount to all students. This means Julie only has to pay 90% of the original cost.
So, the cost of the flute after applying the student discount is: 0.90X dollars.
Step 2: Applying the back to school sale discount
During the back to school sale, an additional 15% discount is given. Again, Julie only has to pay 85% of the price after the student discount.
So, the cost of the flute after applying both discounts is: 0.85 * 0.90X dollars.
According to the given information, Julie purchased the flute for $306. Therefore, we can set up the equation:
0.85 * 0.90X = 306
Now, we can solve for X, which will give us the original cost of the flute:
0.85 * 0.90X = 306
0.765X = 306
X = 306 / 0.765
X ≈ $400
Hence, the original cost of the flute was approximately $400.
306*0.10= ANSWER (10% is 10/100 or 0.10)
ANSWER*0.15 (15% is 15/100 or 0.15)