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
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: $\boxed{400}$.
To determine the original cost of the flute, we need to reverse the sequence of discounts.
First, let's consider the second discount of 15%. We know that after this discount, Julie paid $306 for the flute.
So, to find the price after the second discount, we can set up the following equation:
(100% - 15%) * P = $306
Simplifying:
85% * P = $306
Next, we need to find the price before the first discount of 10%.
To do this, we can divide the result from the previous equation by (100% - 10%):
P = $306 / (100% - 10%)
Simplifying:
P = $306 / 90%
Now, let's calculate the value of P:
P = $306 / 0.9
P = $340
Therefore, the original cost of the flute was $340.
Let's work through the problem step-by-step.
Step 1: Calculate the discounted price after the 10% student discount.
If the original cost is x, then the discounted price is (x - 10% of x).
Step 2: Calculate the discounted price after the additional 15% off during the back to school sale.
If the discounted price after the student discount is y, then the price after the back to school sale is (y - 15% of y).
Step 3: Set up the equation based on the given information.
We know that Julie purchased the flute for $306, so we can set up the equation: (y - 15% of y) = $306.
Step 4: Solve the equation to find the value of y.
To solve the equation, first subtract 15% of y from y: y - 0.15y = $306. Simplifying this, we get 0.85y = $306. Divide both sides by 0.85: y = $360.
Step 5: Calculate the original cost (x) using the student discount of 10% off.
If the discounted price after the student discount is $360, then we can set up the equation: (x - 10% of x) = $360.
Step 6: Solve the equation to find the value of x.
To solve the equation, first subtract 10% of x from x: x - 0.10x = $360. Simplifying this, we get 0.90x = $360. Divide both sides by 0.90: x = $400.
Therefore, the original cost of the flute was $400.
So, the correct answer is 400.