Problem 115 - Elementary Algebra

Question

A grocery store reduced the price of a loaf of bread from \(\$ 2.80\) to \(\$ 2.73\). Find the percent decrease.

Step-by-Step Solution

Answer

The percent decrease is 2.5%.

Step 1 - Identify Initial and Final Prices

The initial price of the loaf of bread was \( \(2.80 \) and the final price is \( \)2.73 \).

Step 2 - Calculate the Price Decrease

Subtract the final price from the initial price: \( 2.80 - 2.73 = 0.07 \). The price decreased by \( $0.07 \).

Step 3 - Divide the Decrease by the Initial Price

To find the percent decrease, divide the decrease in price by the initial price: \( \frac{0.07}{2.80} = 0.025 \).

Step 4 - Convert to Percentage

Multiply the result by 100 to convert the decimal to a percentage: \( 0.025 \times 100 = 2.5 \% \). The percent decrease is 2.5%.

Key Concepts

price reduction

Understanding a price reduction is very important when it comes to being a smart shopper.
A price reduction occurs when the original price of an item is lowered, making it cheaper for consumers.
This can be due to discounts, sales, or clearance events.
In this exercise, the loaf of bread was originally priced at \(\$2.80\) and was reduced to \(\$2.73\).
This change in price can lead to significant savings over time, especially for frequently bought items.
Knowing how to calculate a price reduction helps consumers see how much they are saving, fostering financial awareness and smarter spending habits.

percentage calculation

Calculating the percentage decrease is crucial for comparing the extent of reductions across different scenarios.
Follow these simple steps:
1. Identify the initial and final prices.
For the loaf of bread, the initial price is \(\$2.80\) and the final price is \(\$2.73\).
2. Calculate the absolute decrease in price by subtracting the final price from the initial price:
\(2.80 - 2.73 = 0.07\)
The price decreased by \(\$0.07\).
3. Find the relative decrease by dividing the absolute decrease by the initial price:
\(\frac{0.07}{2.80} \).
4. Convert the result to a percentage by multiplying by 100:
\(0.025 \times 100 = 2.5\)%
The percent decrease is 2.5%.
This method is applicable to any similar problems involving percentage changes.

basic arithmetic

Basic arithmetic forms the foundation of almost all math problems.
In this exercise, we used subtraction and division to solve the problem.
Here's a quick refresh:
- Subtraction: Take the initial price and subtract the final price to get the difference. For instance, \(2.80 - 2.73 = 0.07\).
- Division: Divide the price decrease by the initial price to see how much this decrease represents compared to the original price.
By using these fundamental math operations, we solved the problem step-by-step. If you're comfortable with these basic arithmetic operations, tackling percentage problems becomes much easier.