Problem 5 - 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 \(G\). \(H=40\) hours and \(R=\$ 6\)

Step-by-Step Solution

Answer

The gross pay \(G\) is \(240\) dollars.

Step 1: Understand the Formula

The formula given is \(G = H \cdot R\), where \(G\) is the gross pay, \(H\) is the number of hours worked, and \(R\) is the hourly rate of pay.

Step 2: Substitute the Known Values

Substitute \(H = 40\) hours and \(R = 6\) dollars per hour into the formula: \(G = 40 \cdot 6\).

Step 3: Calculate the Product

Multiply the values: \(40 \cdot 6 = 240\).

Step 4: Interpret the Result

The calculated \(G = 240\) represents the gross pay in dollars for working 40 hours at an hourly rate of $6.

Key Concepts

Hourly Rate

In the world of work, the term **hourly rate** is frequently mentioned, and it plays a crucial role in understanding how wages are computed. Essentially, the hourly rate is the amount of money a person earns for each hour of work performed. It is a commonly used method for compensating employees, particularly in jobs where hours might vary from week to week.

When someone begins working at a job, they often agree on an hourly rate. For instance, if you work as a cashier at a grocery store, your employer might pay you $6 for every hour you work. This rate is vital in calculating your total earnings.

It's important to note that the hourly rate can be influenced by several factors:

• Job type and industry standards
• Employee experience and skill level
• Economic conditions and minimum wage laws

This concept not only helps in determining gross pay but also assists in budgeting personal finances effectively.

Gross Pay Calculation

Figuring out your gross pay is a fundamental skill. Gross pay is the total amount of money you earn from your job before any deductions (like taxes or insurance) are taken out. To calculate your gross pay when you’re paid hourly, you simply need to multiply the number of hours worked by your hourly rate.

Let's say you're working 40 hours a week, and your hourly rate is $6. The gross pay would be calculated as follows:

• Formula: \(G = H \cdot R\)
• Where \(H = 40\) and \(R = 6\)
• Calculation: \(G = 40 \cdot 6 = 240\)

In this calculation, \(G = 240\) represents the gross pay, making this the amount you earn before any fees or taxes are subtracted. Understanding this is key not only for receiving your paycheck but also for managing your finances and knowing what base amount to expect.

Substitution in Algebra

When solving algebraic expressions like \(G = H \cdot R\), substitution is a valuable technique. Substitution involves replacing variables with known values to simplify and solve an equation. In our exercise concerning gross pay, we use substitution to find \(G\) by inserting the values for \(H\) and \(R\).

Let's break this down:

• You have the formula \(G = H \cdot R\).
• Given: \(H = 40\) and \(R = 6\).
• Substitution: Replace \(H\) and \(R\) with these values, so the equation becomes \(G = 40 \cdot 6\).

This substitution is crucial because it takes a general formula and turns it into a specific calculation you can easily compute. It transforms abstract algebraic expressions into concrete numbers, helping us find solutions more readily. This method is invaluable in many areas of math, physics, and even real-world applications.