Harriet Earns The Same Amount Of Money Each Day. Her Gross Pay At The End Of 7 Workdays Is $35h + 56$ Dollars. Which Expression Represents Her Gross Pay Each Day?A. $5h + 8$B. \$8h + 5$[/tex\]C. $7h +
Introduction
In this article, we will delve into a mathematical problem that involves finding the daily gross pay of an individual, Harriet, who earns the same amount of money each day. The problem states that her gross pay at the end of 7 workdays is represented by the expression $35h + 56$ dollars. Our goal is to determine which expression represents her gross pay each day.
Understanding the Problem
To solve this problem, we need to understand the concept of gross pay and how it relates to the number of workdays. Gross pay refers to the total amount of money earned by an individual before any deductions, such as taxes or benefits. In this case, Harriet's gross pay is represented by the expression $35h + 56$ dollars, where $h$ represents the number of hours worked.
Breaking Down the Expression
Let's break down the expression $35h + 56$ dollars to understand its components. The first part, $35h$, represents the total amount of money earned by Harriet for working $h$ hours. The second part, $56$, represents a fixed amount of money that Harriet earns, regardless of the number of hours worked.
Finding the Daily Gross Pay
To find Harriet's daily gross pay, we need to divide the total gross pay by the number of workdays. In this case, we are given that Harriet works for 7 days. Therefore, we can divide the expression $35h + 56$ dollars by 7 to find her daily gross pay.
Calculating the Daily Gross Pay
To calculate the daily gross pay, we can use the following formula:
Daily Gross Pay = (Total Gross Pay) / Number of Workdays
In this case, the total gross pay is represented by the expression $35h + 56$ dollars, and the number of workdays is 7. Therefore, we can write the formula as:
Daily Gross Pay = ($35h + 56$) / 7
To simplify the expression, we can divide both the numerator and the denominator by 7:
Daily Gross Pay = ($5h + 8$) / 1
Since we are dividing by 1, the expression remains the same. Therefore, Harriet's daily gross pay is represented by the expression $5h + 8$ dollars.
Conclusion
In conclusion, we have successfully solved the problem of finding Harriet's daily gross pay. By breaking down the expression $35h + 56$ dollars and dividing it by the number of workdays, we found that Harriet's daily gross pay is represented by the expression $5h + 8$ dollars.
Answer
The correct answer is:
A. $5h + 8$
Discussion
This problem requires a basic understanding of algebra and the concept of gross pay. It also requires the ability to break down complex expressions and simplify them. The problem is relevant to real-world scenarios, such as calculating daily wages or salaries.
Related Problems
This problem is related to other mathematical concepts, such as:
- Algebra: The problem requires the use of algebraic expressions and equations to solve.
- Gross Pay: The problem involves calculating gross pay, which is a common concept in finance and accounting.
- Division: The problem requires dividing a complex expression by a number to find the daily gross pay.
Tips and Tricks
To solve this problem, you can use the following tips and tricks:
- Break down complex expressions: Break down the expression $35h + 56$ dollars into its components to understand its structure.
- Use algebraic properties: Use algebraic properties, such as the distributive property, to simplify the expression.
- Check your work: Check your work by plugging in values for $h$ to ensure that the expression is correct.
Introduction
In our previous article, we solved the problem of finding Harriet's daily gross pay. We broke down the expression $35h + 56$ dollars and divided it by the number of workdays to find that Harriet's daily gross pay is represented by the expression $5h + 8$ dollars. In this article, we will answer some frequently asked questions related to this problem.
Q&A
Q: What is the total gross pay for 7 workdays?
A: The total gross pay for 7 workdays is represented by the expression $35h + 56$ dollars.
Q: How do I calculate the daily gross pay?
A: To calculate the daily gross pay, you need to divide the total gross pay by the number of workdays. In this case, you can use the formula:
Daily Gross Pay = (Total Gross Pay) / Number of Workdays
Q: What is the daily gross pay for 1 workday?
A: The daily gross pay for 1 workday is represented by the expression $5h + 8$ dollars.
Q: How do I simplify the expression $35h + 56$ dollars?
A: To simplify the expression $35h + 56$ dollars, you can divide both the numerator and the denominator by 7:
Daily Gross Pay = ($35h + 56$) / 7
Q: What is the relationship between the total gross pay and the daily gross pay?
A: The total gross pay is the sum of the daily gross pay multiplied by the number of workdays. In this case, the total gross pay is $35h + 56$ dollars, and the daily gross pay is $5h + 8$ dollars.
Q: How do I check my work?
A: To check your work, you can plug in values for $h$ to ensure that the expression is correct. For example, if $h = 1$, the total gross pay is $35(1) + 56 = 91$ dollars, and the daily gross pay is $5(1) + 8 = 13$ dollars.
Q: What are some real-world applications of this problem?
A: This problem has real-world applications in finance and accounting, such as calculating daily wages or salaries.
Conclusion
In conclusion, we have answered some frequently asked questions related to the problem of finding Harriet's daily gross pay. By breaking down complex expressions and using algebraic properties, we can simplify the expression and find the daily gross pay.
Related Problems
This problem is related to other mathematical concepts, such as:
- Algebra: The problem requires the use of algebraic expressions and equations to solve.
- Gross Pay: The problem involves calculating gross pay, which is a common concept in finance and accounting.
- Division: The problem requires dividing a complex expression by a number to find the daily gross pay.
Tips and Tricks
To solve this problem, you can use the following tips and tricks:
- Break down complex expressions: Break down the expression $35h + 56$ dollars into its components to understand its structure.
- Use algebraic properties: Use algebraic properties, such as the distributive property, to simplify the expression.
- Check your work: Check your work by plugging in values for $h$ to ensure that the expression is correct.
By following these tips and tricks, you can successfully solve this problem and find Harriet's daily gross pay.