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 solve this problem, we need to determine how much Harriet earns each day based on the information given about her total earnings after 7 workdays.
Problem Breakdown:
- Harriet earns the same amount each day.
- After 7 workdays, her gross pay is represented by the expression $35h + 56$ dollars.
Step-by-step Explanation:
- Identify the Total Gross Pay:
The total gross pay for 7 workdays is given as $35h + 56$. - Find the Daily Earnings:
Since Harriet earns the same amount each day, her gross pay for one day would be the same for all 7 days. We need to find the daily earnings, which is represented as an expression. To do this, we divide the total gross pay by 7, since her pay is constant each day. This gives us the following equation: $$
\text{Daily Pay} = \frac{35h + 56}{7}
$$ - Simplify the Expression:
Now, we simplify the expression by dividing each term inside the parentheses by 7. $$
\frac{35h}{7} + \frac{56}{7}
$$ Simplifying each term: $$
\frac{35h}{7} = 5h \quad \text{and} \quad \frac{56}{7} = 8
$$ So, the simplified expression for Harriet’s daily pay is: $$
5h + 8
$$
Final Answer:
The expression that represents Harriet’s gross pay each day is $\boxed{5h + 8}$.
Explanation of the Result:
- Harriet earns $5h + 8$ dollars each day.
- The term $5h$ represents a portion of her daily earnings that depends on the variable $h$, and the term $8$ represents a fixed amount of money she earns each day in addition to the variable part.
- By dividing her total earnings over the 7 days by 7, we were able to find her daily earnings in a simpler form. This ensures that $5h + 8$ accurately reflects the amount Harriet earns per day.