Question

Economics Caroline needs a new winter coat. The Winter Warehouse advertises that everything in the store is \(75 \%\) of the retail price. Coats Galore advertises that all its coats are on sale for \(\frac{7}{10}\) of the retail price. If the stores carry the same brands, where will Caroline find better prices? Explain.

Short answer

Winter Warehouse offers better prices because 0.25 is less than 0.7.

Step-by-step solution

Define the Discounts

Identify the discounts offered by each store. Winter Warehouse offers a discount of 75% of the retail price, which means the customer pays 25% of the retail price. Coats Galore offers a discount where the customer pays \( \frac{7}{10} \) of the retail price.

Convert the Discounts to Decimals

Express the percentages as decimals. For Winter Warehouse, the customer pays 25% of the retail price, which is 0.25. For Coats Galore, the customer pays \( \frac{7}{10} \) of the retail price, which is 0.7.

Compare the Prices

Compare the decimal values. The Winter Warehouse's price factor is 0.25, whereas Coats Galore's price factor is 0.7. Since 0.25 is less than 0.7, Winter Warehouse offers a better price.

Conclude the Better Store

Determine where Caroline will find better prices. Since Winter Warehouse has a lower price factor (0.25) compared to Coats Galore (0.7), Caroline will find a better price at Winter Warehouse.

Key concepts

Discount Calculation

When calculating discounts, it's essential to understand how much you'll be paying after the discount is applied.
Let's break this down using our example.
The Winter Warehouse offers everything at 75% off. This means you pay 25% of the item's retail price.
For Coats Galore, you pay \( \frac{7}{10} \) or 70% of the retail price.
To find out how much you're paying, you first need to subtract the discount from 100%. This gives you the percentage of the original price you'll be paying.

Comparing Prices

To figure out where you'll pay less, you need to compare the actual amount paid after the discounts.
In our example, Winter Warehouse and Coats Galore offer the same coat brands.
Comparing prices involves looking at the percentages you're paying after applying the discounts.
For Winter Warehouse, paying 25% of the retail price (which is 0.25 in decimal form) compared to Coats Galore's 70% (which is 0.7 in decimal form). Clearly, 0.25 is less than 0.7, so Winter Warehouse offers the better deal.

Decimal Conversion

Decimal conversion is a helpful tool in comparing percentage values.
To convert a percentage to a decimal, simply divide the percentage by 100.
For instance:

• 25% becomes 0.25 because \( 25 / 100 = 0.25 \).
• 70% becomes 0.7 because \( 70 / 100 = 0.7 \).

This conversion allows easier comparison between different values by making the math simpler.

Percentage

The concept of percentage is critical in many real-life math problems, especially during sales and discounts.
Percentages are simply parts of 100. So, 25% means 25 out of 100, while 70% means 70 out of 100.
When a store offers a sale, they're showing a percentage of the price you’ll pay.
Understanding percentages helps you quickly determine the better deal, just like how Caroline figured out that Winter Warehouse had the lower percentage to pay compared to Coats Galore.