Calculating the Original Price of a CD with Sales Tax

In today's lesson, we will explore how to calculate the original price of a CD when given the total price including sales tax. This is a practical skill that can be useful in understanding the economics behind purchases. Let's dive into the problem and see how to solve it step by step.

The Problem

Evan buys a new CD and pays $15 in sales tax. If the sales tax rate is 2.4%, what is the original price of the CD?

Solution Methods

Method 1: Proportional Calculation

To solve this problem, we can use a simple proportional calculation. Let's break it down step by step:

Let the original price of the CD be X. The sales tax paid is given as $15, and the tax rate is 2.4%, or 2.4/100 (or 2.4%).

We can set up the proportion as follows:

15 —————- 2.4 100 ————- X

Solving for X, we get:

X 100 times; 2.4 / 15 X 16

Method 2: Quick Calculation

For a faster answer, we can use the division directly:

2.4 / 0.15 16

This method works because 2.4 (sales tax) divided by the tax rate (0.15) gives us the original price.

Method 3: Long Calculation Without a Calculator

Another method is to break the calculation into steps without using a calculator:

Original value: 100 15 2.4 Double: 30 4.8 Divide by 3: 10 1.6 Multiply by 10: 100 16

Thus, the original price of the CD is 16.

Verification

To verify our calculations, we can recheck the proportion:

2.4 is 15% of 16:

0.15 times; 16 2.4

Conclusion

The original price of the CD, given the sales tax of $15 and a tax rate of 2.4%, is $16. It's important to note that while the tax paid indicates the original price based on the tax rate, other factors like discounts could affect the final price Evan paid.