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 determine Harriet’s daily gross pay, we start with the information that her total gross pay over 7 workdays is represented by the expression $35h + 56$ dollars. Since she earns the same amount each day, we can find her daily earnings by dividing the total gross pay by the number of workdays:
$$
\text{Daily Gross Pay} = \frac{35h + 56}{7}
$$
To simplify this expression, we divide each term in the numerator by 7
$$
\frac{35h}{7} + \frac{56}{7} = 5h + 8
$$
Therefore, the expression representing Harriet’s gross pay each day is $5h + 8$.
Detailed Explanation
Understanding the Problem:
Harriet’s total earnings over 7 days are given by the algebraic expression $35h + 56$. This expression suggests that her pay comprises two components: a variable part ($35h$) and a fixed part (56). The variable part likely depends on the number of hours worked or a similar factor represented by $h$, while the fixed part could represent a consistent daily allowance or bonus.
Calculating Daily Earnings:
Since Harriet earns the same amount each day, we divide her total earnings by 7 to find her daily pay:
$$
\frac{35h + 56}{7}
$$
Using the distributive property of division over addition, we split the expression:
$$
\frac{35h}{7} + \frac{56}{7}
$$
Simplifying each term:
- $\frac{35h}{7} = 5h$
- $\frac{56}{7} = 8$
Combining these results gives:
$$
5h + 8
$$
Interpretation:
The simplified expression $5h + 8$ indicates that Harriet’s daily gross pay consists of a variable component ($5h$) and a fixed component (8). This structure is common in compensation models where employees receive a base pay plus additional earnings based on performance metrics like hours worked or units produced.
Conclusion:
By dividing the total earnings expression $35h + 56$ by 7, we determine that Harriet’s daily gross pay is represented by the expression $5h + 8$.