Problem 110 - Elementary Algebra

Question

Ayodele got a raise in her hourly pay, from \(\$ 24.50\) to \(\$ 25.48\). Find the percent increase.

Step-by-Step Solution

Answer

Approximately 4%.

Step 1 - Identify the initial and new hourly pay

Ayodele's initial hourly pay is \(\$ 24.50\), and her new hourly pay is \(\$ 25.48\).

Step 2 - Calculate the increase in hourly pay

Subtract the initial hourly pay from the new hourly pay: \(25.48 - 24.50 = 0.98\). The increase in hourly pay is \(\$ 0.98\).

Step 3 - Calculate the percent increase

Use the formula for percent increase: \[\text{Percent Increase} = \frac{\text{Increase}}{\text{Initial Pay}} \times 100\] Substituting the values, we get: \[\text{Percent Increase} = \frac{0.98}{24.50} \times 100 \approx 4\text{%}\]

Key Concepts

percent change

In this section, we'll dive into what percent change means and how it’s calculated. The percent change formula is used to determine how much a value has increased or decreased in comparison to its initial value. This is particularly useful to compare changes over time or after an event, such as a pay raise or decrease.

To find percent change, we use the following formula:
\[\text{Percent Change} = \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100\]

When applying this concept to Ayodele's hourly pay increase from \$24.50\ to \$25.48\, we can use the exact formula by substituting the values:
\[\text{Percent Increase} = \frac{25.48 - 24.50}{24.50} \times 100\]

This helps us to see the relative growth, which is especially useful for understanding changes in pay, prices, or other measurable quantities.

increase calculation

Understanding how to calculate an increase is essential, especially in financial contexts. Here, we focus on determining the actual increase before converting it to a percent change.

To calculate the increase, follow these steps:

• Identify the new value and the initial value.
• Subtract the initial value from the new value.

This difference is the actual increase. Let's apply this to Ayodele's pay raise.

Her initial pay was \$24.50\ and her new pay is \$25.48\. Using the formula:
\[\text{Increase} = 25.48 - 24.50 = 0.98\]

This reveals that Ayodele's hourly pay increased by \$0.98\, which we will need for the percent change calculation.

basic algebra

Algebra forms the foundation for many mathematical calculations, including those related to percent change and increase calculation. In our example, we used basic algebraic operations such as subtraction, division, and multiplication.

Let's break down the steps to solve the problem using algebra:

• First, we identified the variable quantities, Ayodele's initial pay \$24.50\ and her new pay \$25.48\.
• Next, we calculated the difference between the new and initial pay using subtraction: \$25.48 - 24.50 = 0.98\.
• Finally, to find the percent increase, we used division and multiplication: \[\frac{0.98}{24.50} \times 100 \text{ to get an approximate 4\text{% increase}\].

This algebraic understanding allows us to convert raw numbers into meaningful insights, like determining the percent increase in pay.