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 Harriet’s daily gross pay, we are told that over 7 workdays she earns a total of 35h + 56 dollars. Since she earns the same amount each day, we can simply divide the total gross pay by 7 to find her daily pay.
Step-by-Step Solution:
Total gross pay for 7 days:
[
35h + 56
]
To find her daily pay, divide this expression by 7:
[
\frac{35h + 56}{7}
]
Now divide each term separately:
[
\frac{35h}{7} + \frac{56}{7} = 5h + 8
]
✅ Correct Answer:
[
\boxed{5h + 8}
]
📘 Explanation (Approx. 300 words):
In this problem, we’re working with an algebraic expression that represents a total amount of money Harriet earns over 7 days. We are told she earns the same amount each day, and the total amount she earns is given as 35h + 56 dollars. This expression likely includes a variable (h) that could represent something like hourly wage or hours worked per day, but we don’t need to know exactly what h means to solve the problem—we just need to divide the total evenly over 7 days.
When dividing an algebraic expression like 35h + 56 by a constant (in this case, 7), we can divide each part (or term) of the expression separately. This follows the distributive property of division over addition, which states:
[
\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}
]
So:
[
\frac{35h + 56}{7} = \frac{35h}{7} + \frac{56}{7}
]
We simplify:
- ( \frac{35h}{7} = 5h )
- ( \frac{56}{7} = 8 )
Putting it all together, the expression for Harriet’s daily gross pay is 5h + 8.
This new expression means that every day, Harriet earns an amount made up of 5 times h plus 8 dollars. This helps break down her total weekly pay into a consistent daily amount.