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 gross pay each day, we need to divide her total pay over 7 days by the number of days she worked.
Given:
Her gross pay at the end of 7 workdays = 35h + 56
She earns the same amount each day
Number of days worked = 7
To Find:
Her daily gross pay
Solution:
To find the pay per day, divide the total pay by 7:
[
\text{Daily pay} = \frac{35h + 56}{7}
]
We can simplify this expression:
[
\frac{35h + 56}{7} = \frac{35h}{7} + \frac{56}{7} = 5h + 8
]
✅ Final Answer: (\boxed{5h + 8})
✍️ Explanation (300 words):
To determine how much Harriet earns each day, we use the concept of unit rate—that is, the total amount divided by the number of units (in this case, days). The problem tells us that Harriet earns a total of 35h + 56 dollars after working for 7 days, and that she earns the same amount every day. That means the total pay is evenly distributed across all 7 days.
To find out her daily earnings, we divide the total expression by 7. Mathematically, this looks like:
[
\frac{35h + 56}{7}
]
This is a typical algebraic division problem. The key step here is to apply the distributive property of division over addition, which allows us to divide each term in the numerator separately by the denominator. That gives:
[
\frac{35h}{7} + \frac{56}{7}
]
Next, simplify each term:
- ( \frac{35h}{7} = 5h )
- ( \frac{56}{7} = 8 )
So, Harriet earns 5h + 8 dollars per day.
This expression tells us that her daily income depends on h, where h could represent hours worked, an hourly rate, or another variable factor. The constant 8 represents a fixed amount she earns daily in addition to the variable part.
This method helps us break down a real-world situation using algebra, and shows how expressions can model consistent patterns like daily earnings.
