Problem 6 - Prealgebra

Question

The formula \(G=H \cdot R\) tells us how much gross pay \(G\) a person receives for working \(H\) hours at an hourly rate of pay \(R\).find \(G\). \(H=36\) hours and \(R=\$ 8\)

Step-by-Step Solution

Answer

The gross pay is \(\$288\).

Step 1: Identify the Given Variables

We are given that the number of hours worked, \(H\), is 36 hours, and the hourly rate, \(R\), is \(\$8\).

Step 2: Use the Formula

The formula provided is \(G = H \cdot R\), which relates gross pay \(G\) to hours worked \(H\) and hourly rate \(R\).

Step 3: Substitute the Given Values

Substitute the given values into the formula: \(G = 36 \cdot 8\).

Step 4: Calculate the Product

Multiply the number of hours by the rate: \(36 \times 8 = 288\).

Step 5: State the Final Answer

The gross pay \(G\) is \(\\(288\) when \(H = 36\) and \(R = \\)8\).

Key Concepts

Calculation Steps

In math, calculation steps are like a recipe; they provide a clear path to reaching a solution. It's essential to follow them to ensure accuracy.

• **Identify Variables**: Begin by pinpointing the values given in the problem. In our example, these are the hours worked, \(H\), and the hourly rate, \(R\).
• **Apply the Formula**: Use the appropriate formula. Here, it is \(G = H \cdot R\). This formula connects the hours worked and hourly rate to calculate gross pay.
• **Substitute Values**: Insert the given numbers into the formula. In this scenario, substituting \(H = 36\) and \(R = 8\) is key.
• **Calculate**: Perform the necessary arithmetic to find the solution. Multiplication is straightforward, but it's crucial to check work.
• **Verify and State**: After computing, double-check the calculation. State the final answer as the last step to confirm understanding.

Each step builds on the previous, leading to a correct and complete solution. Remember, practice builds confidence and accuracy.

Hourly Wage Calculation

Calculating hourly wage is a fundamental skill that helps understand earnings and budgeting. The concept revolves around the formula \(G = H \cdot R\), where:

• \(G\) is the gross pay
• \(H\) represents hours worked
• \(R\) is the rate per hour

To find the gross pay, multiply the total hours worked by the hourly rate. For example, working 36 hours at an \(8 rate results in a gross pay of \)288. These calculations are not only practical for tracking earnings but are also used in various job sectors.Learning to apply this calculation in real-life scenarios can aid in better financial planning and understanding the impact of different variables like working more hours or earning a higher hourly rate. Being comfortable with this math concept can make budgeting and income projections more accurate and realistic.

Problem Solving in Math

Math problem solving is all about strategizing and applying knowledge to attain solutions. It has four stages: understanding, planning, executing, and reviewing.

• **Understanding the Problem**: Comprehend what is being asked. Knowing what the variables represent is part of this phase. In our example, understanding \(H\), \(R\), and \(G\) is vital.
• **Planning**: Determine which mathematical processes to use. Her,e the use of the \(G = H \cdot R\) formula is chosen.
• **Executing**: Carry out calculations. Substitute numbers and perform arithmetic, ensuring precision in each step.
• **Reviewing**: Check calculations for mistakes and ensure the solution addresses the original problem.

Effective problem solving enhances critical thinking and often involves circular thinking—where checking an answer may lead back to reassessment of the problem and plan if errors are found. Practice helps in refining these skills, making them useful beyond the math classroom.