Problem 52 - Algebra 1

Question

You get paid $152.25 for working 21 hours. Find your hourly rate of pay.

Step-by-Step Solution

Answer

Your hourly rate of pay is $7.25 per hour.

Step 1: Identify Given Values

The total pay earned is $152.25 and the total hours worked is 21 hours.

Step 2: Set Up the Formula

The formula to calculate the hourly rate of pay is Hourly Rate = Total Pay / Total Hours Worked.

Step 3: Insert Given Values

Substitute the given values into the formula: Hourly Rate = $152.25 / 21 hours.

Step 4: Calculate

Perform the division operation: Hourly Rate = $7.25 per hour

Key Concepts

Rate of Pay

Understanding the rate of pay is essential for employees and freelancers alike. It represents the amount of money earned per hour of work. Knowing how to calculate and interpret your rate of pay can be important for budgeting and financial planning. In the provided exercise, the rate of pay is determined by dividing the total compensation received by the number of hours worked, which allows one to understand their remuneration for each hour of labor.

It's good practice to regularly review your hourly rate, especially after taking on additional responsibilities or gaining more experience, to ensure fair compensation for your time and effort. Employers also use the rate of pay to structure compensation packages and align them with industry standards.

Hourly Wage Calculation

Calculating your hourly wage is a straightforward but vital arithmetic task. This calculation helps workers see what they're earning on an hourly basis, no matter how many hours they work each week. The formula used for hourly wage calculation aligns with the exercise: divide your total pay by the number of hours worked.

For anyone learning about finances, knowing how to compute your hourly wage can also be beneficial when comparing job offers or negotiating salaries. It's also useful for freelance or contract workers who need to set their rates based on the market and their skills.

Algebraic Problem Solving

Algebraic problem solving encompasses identifying variables, expressing relationships through equations, and manipulating these equations to find a solution. In the context of calculating an hourly rate, the problem simplifies to a basic algebraic equation. The total pay serves as the product of the hourly rate and the hours worked.

Understanding algebra is key to solving a variety of real-life problems, from personal finance to engineering. This exercise serves as a practical example of how algebra is applied in everyday scenarios, reinforcing the relevance of mathematical literacy in the workforce and personal money management.

Division Operation

The division operation is one of the four fundamental arithmetic operations, and it's used to distribute a number into equal parts. In our example, division is used to spread the total income across the total hours worked to find the rate of pay per hour. The division is represented by the slash symbol (/) or the division sign (÷).

It's often paired with multiplication, its inverse operation, to solve for unknowns in equations. Mastery of division is not only critical for mathematical proficiency but is also immensely practical when evaluating proportions, rates, and densities in various contexts.