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?
The correct answer and explanation is :
To find the expression representing Harriet’s gross pay each day, we need to break down the problem carefully.
Step 1: Understanding the given information
The problem states that Harriet’s gross pay at the end of 7 workdays is represented by the expression:
[
35h + 56 \, \text{dollars}
]
This is her total pay for 7 workdays. The goal is to find the amount she earns each day. Since Harriet earns the same amount each day, her total pay for 7 days is the product of her daily earnings and 7. Let’s define her daily earnings as d (in dollars).
So, her total pay for 7 workdays can be written as:
[
7d = 35h + 56
]
Step 2: Solve for d (her daily earnings)
To find the daily earnings, we need to solve for d. To do this, we simply divide both sides of the equation by 7:
[
d = \frac{35h + 56}{7}
]
Now, we simplify the right-hand side of the equation:
[
d = \frac{35h}{7} + \frac{56}{7}
]
[
d = 5h + 8
]
So, Harriet earns 5h + 8 dollars each day.
Step 3: Conclusion
The expression representing Harriet’s gross pay each day is:
[
5h + 8
]
This means that for each day she works, Harriet earns an amount that is 5 times h plus 8 dollars.
Explanation of the solution
The key to solving this problem was recognizing that Harriet’s total pay for 7 workdays, 35h + 56, is the result of multiplying her daily pay by 7. From there, we solved for her daily pay by dividing the total by 7 and simplifying the expression. The solution 5h + 8 indicates that her daily pay depends on some factor h, and it is always 8 dollars more than 5 times h.
