Question

Solve. A social worker worked a total of 1259 cases in one year. The next year he worked 1540 cases. What was the percent of increase in caseload?

Short answer

Answer: The approximate percent increase in caseload is 22.32%.

Step-by-step solution

Find the difference in caseload

Subtract the first year's caseload from the second year's caseload to find the difference: difference = 1540 - 1259

Calculate the percent of increase

Divide the difference by the original (first year's) caseload and multiply by 100: percent_increase = (difference / 1259) * 100

Simplify the expression

First, calculate the difference: difference = 1540 - 1259 = 281 Now, calculate the percent_increase: percent_increase = (281 / 1259) * 100

Solve for the percent of increase

Divide 281 by 1259 and then multiply by 100: percent_increase = (281 / 1259) * 100 ≈ 22.32% The percent of increase in caseload is approximately 22.32%.

Key concepts

Percentage Calculation

Understanding the calculation of percentages is essential for interpreting changes between two values, such as understanding financial growth, scoring in exams, or, in our example, a change in caseload for a social worker.

To find the percentage increase, you need to know two figures: the original number and the new number. You subtract the original number from the new number to find the difference, then divide this difference by the original number. To convert this into a percentage, you multiply the result by 100. This is represented by the formula:
\[\text{Percentage Increase} = \left( \frac{\text{New Number} - \text{Original Number}}{\text{Original Number}} \right) \times 100\]
If the result is a positive number, it indicates an increase. If it is negative, it indicates a decrease. Calculating percentage increases helps you understand the scale of change in a clear, consistent manner.

Numerical Problem Solving

Numerical problem solving involves taking real-world scenarios and using numbers and operations to solve a question or problem. It's not just about finding an answer, but about understanding the process and using the correct operations at the correct step. In our caseload example, there are clear steps taken to solve the problem: finding the difference between two numbers, dividing by the original number, and then converting to a percentage.

It's vital to follow a systematic approach when solving such numerical problems:

• Identify the values given,
• Determine the relationship between the values,
• Apply the correct formulas,
• Carefully perform each operation in order,
• Check the answer for reasonableness.

This methodical approach ensures accuracy and enhances your ability to tackle a variety of quantitative challenges.

Mathematical Reasoning

Mathematical reasoning is the logical process used to arrive at a conclusion based on the numerical evidence at hand. It is fundamental in validating the steps of any mathematical problem, including those involving percentage increase. In our caseload example, reasoning is used to interpret the meaning behind the 22.32% increase. We have to ask: Is this percentage significant? What might be the implications of this increase for the social worker's workload?

Throughout mathematical processes, reasoning also helps us understand why we perform certain operations. For instance, why do we multiply by 100 in our percentage formula? It's because a percentage is a fraction of 100, so to convert our decimal to a percentage, we bring the value into the context of 100 parts. This kind of reasoning solidifies understanding and drives the real-world application of math. It ensures that the solutions are not just numbers but meaningful figures that can influence decision-making and assessments.