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 :
Let’s start with the correct answer first:
Correct Answer:
Her gross pay at the end of 7 days is ( 35h + 56 ) dollars.
Since she earns the same amount each day, we divide the total gross pay by 7 to find her daily pay:
[
\text{Daily gross pay} = \frac{35h + 56}{7}
]
Now, let’s simplify:
First, divide each term in the numerator by 7 separately:
[
\frac{35h}{7} + \frac{56}{7} = 5h + 8
]
Thus, Harriet’s gross pay each day is ( 5h + 8 ) dollars.
Explanation (about 300 words):
Harriet earns the same amount of money each day, which means her daily gross pay is consistent. The information given states that after 7 workdays, her total gross pay is represented by the algebraic expression ( 35h + 56 ).
To find how much she earns in one day, we need to divide her total gross pay by the number of workdays, which is 7. This is because earning the same amount daily over several days means the total is simply 7 times her daily earnings. To reverse this multiplication and isolate the amount for one day, we divide by 7:
[
\frac{35h + 56}{7}
]
When dividing an algebraic expression by a number, we divide each term separately. So:
- ( \frac{35h}{7} = 5h )
- ( \frac{56}{7} = 8 )
Thus, when simplified, her daily earnings are:
[
5h + 8
]
This means every day Harriet earns an amount that depends on the variable ( h ) — specifically, five times ( h ) dollars plus an extra 8 dollars.
It’s important to simplify correctly because this reflects how algebraic expressions behave under operations like addition, multiplication, and division. Algebra is about recognizing patterns and applying operations consistently.
In real life, this kind of problem helps us understand pay structures, budgeting, and rates of change. Harriet’s daily income isn’t just a fixed number—it changes depending on ( h ), which could represent hours worked, an hourly rate, or another variable factor in her pay.