Problem 134 - Elementary Algebra

Question

Sophie saw a dress she liked on sale for \(\$ 15\) off. The original price of the dress was \(\$ 96\).

Step-by-Step Solution

Answer

The sale price is \$ 81.

Step 1 - Identify the original price

The original price of the dress is given as \(\text{original price} = \$ 96\).

Step 2 - Identify the discount

The discount offered on the dress is \(\text{discount} = \$ 15\).

Step 3 - Calculate the sale price

Subtract the discount from the original price to find the sale price. \(\text{sale price} = \text{original price} - \text{discount}\).\(\text{sale price} = \$ 96 - \$ 15 = \$ 81\).

Key Concepts

Discount Calculation

Calculating a discount is one of the most common tasks in shopping math. It's important to understand how to correctly subtract a discount amount from the original price. In this exercise, the dress Sophie likes has a discount of \$15\. The original price is \$96\.

To find out the final sale price, we need to subtract the discount from the original price:
\[ \text{sale price} = \text{original price} - \text{discount} \]
Plugging in the numbers, we get:
\[ \text{sale price} = 96 - 15 = 81 \]

So, the sale price of the dress is \$81\. This concept of discount calculation is essential, whether you're shopping for clothes, groceries, or electronics. It helps you understand how much money you save and what you’ll actually pay at the checkout.

Basic Arithmetic Operations

In mathematical problems related to shopping, basic arithmetic operations like addition and subtraction are frequently used. Here, we used subtraction to find the sale price of the dress after a discount. The basic steps involve:

• Identifying the original price
• Identifying the discount amount
• Subtracting the discount from the original price to get the sale price

For example, in our problem:
\[ 96 - 15 \]
First, subtract the tens place digit:
\[ 96 - 10 = 86 \]
Then, subtract the remaining amount from that result:
\[ 86 - 5 = 81 \]

This breakdown might seem simple, but mastering these steps ensures you can efficiently tackle any everyday shopping math problem.

Shopping Math

Shopping math is all about applying basic math to everyday scenarios. Knowing how to calculate discounts, sales tax, and total prices helps you make informed purchasing decisions. Let's consider the problem Sophie faced. She encountered a dress originally priced at \$96\ with a discount of \$15\.

To find the discounted price, as we discussed:
\[ \text{sale price} = 96 - 15 = 81 \]

Simple shopping math also includes understanding sales tax or additional fees, which might apply depending on the location. For instance, assuming a sales tax of 8\%, you would calculate it as follows:
\[ \text{sales tax} = \text{sale price} \times \text{tax rate} \]
\[ \text{sales tax} = 81 \times 0.08 = 6.48 \]

So, the total price you pay at checkout would be:
\[ \text{total price} = 81 + 6.48 = 87.48 \]

Knowing these calculations ensures you stay within budget and understand the cost breakdown of your purchases.