91Ó°ÊÓ

When determining the markup rate, the first step is to calculate the increase in price. This is the difference between the new selling price and the original price. In our example, the hairdryer initially costs \(60. The selling price is now \)69. The increase in price is found by subtracting the original price from the selling price. Hence, we have:

Selling price: \(69
Original price: \)60
Increase in price: \[69 - 60 = 9 \]

The increase in price is \(9. This means that the hairdryer is sold for \)9 more than its original cost.

To find how much the price has increased in terms of a percentage, we need to calculate the markup rate. This involves comparing the increase in price to the original price. When we talk about percentages, we're essentially standardizing our value across 100. Here's how to do it:

The formula to find the markup rate is: \[ Markup \, rate = \frac{Increase \, in \, price}{Original \, price} \times 100 \] Using our values for the hairdryer: \[ Markup \, rate = \frac{9}{60} \times 100 \] We can simplify the fraction: \[ \frac{9}{60} = 0.15 \] Now we multiply by 100 to get the percentage: \[ 0.15 \times 100 = 15\text{%} \] Thus, the markup rate is 15%. This means the hairdryer's price increased by 15% from its original value.

It's always important to express the final value as a percentage, as it provides a clearer understanding of the increase relative to the original amount.

Markup calculations rely on basic arithmetic operations, which are crucial in solving these types of problems. Let's break down the arithmetic used in this example:

\ Addition and Subtraction: These operations are used to find the increase in price by subtracting the original price from the selling price: \[69 - 60 = 9 \] \ Fractions and Division: Once the increase is found, we express it as a fraction of the original price and then convert it into a percentage: \[ \frac{Increase \, in \, price}{Original \, price} = \frac{9}{60} \] \ Multiplication: Lastly, we multiply the fraction by 100 to convert the decimal into a percentage: \[ \frac{9}{60} \times 100 = 15\% \]

Understanding these arithmetic operations enables us to decompose complex problems into simpler steps. This foundation is essential in not only markup calculations but also in a wide range of mathematical problems.