Chapter 4: Problem 6
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 \(R=\$ 8\)
Short Answer
Expert verified
The gross pay is \(\$288\).
Step by step solution
01
Identify the Given Variables
We are given that the number of hours worked, \(H\), is 36 hours, and the hourly rate, \(R\), is \(\$8\).
02
Use the Formula
The formula provided is \(G = H \cdot R\), which relates gross pay \(G\) to hours worked \(H\) and hourly rate \(R\).
03
Substitute the Given Values
Substitute the given values into the formula: \(G = 36 \cdot 8\).
04
Calculate the Product
Multiply the number of hours by the rate: \(36 \times 8 = 288\).
05
State the Final Answer
The gross pay \(G\) is \(\\(288\) when \(H = 36\) and \(R = \\)8\).
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
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.
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
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.