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:
Correct Answer: 35h+567\frac{35h + 56}{7}
Explanation (300+ words):
To determine Harriet’s gross pay each day, we need to divide her total pay over 7 workdays by the number of days worked.
The problem tells us that Harriet earns the same amount of money each day, meaning her daily earnings are consistent. It also tells us that after working 7 days, her total or gross pay is: 35h+56 dollars35h + 56 \text{ dollars}
To find the daily earnings (which are the same each day), we perform the operation: Daily Pay=Total PayNumber of Days Worked=35h+567\text{Daily Pay} = \frac{\text{Total Pay}}{\text{Number of Days Worked}} = \frac{35h + 56}{7}
This is an example of using division to find a unit rate, where we divide the total by the number of units (in this case, 7 days) to find the amount for just one unit (1 day).
Let’s simplify the expression: 35h+567\frac{35h + 56}{7}
We divide both terms in the numerator individually by 7:
- 35h7=5h\frac{35h}{7} = 5h
- 567=8\frac{56}{7} = 8
So the expression simplifies to: 5h+85h + 8
This means Harriet earns 5h + 8 dollars per day.
Thus, the expression that initially represents her gross pay each day is: 35h+567\frac{35h + 56}{7}
And the simplified expression is: 5h+85h + 8
So either answer may be used depending on the context, but if the question specifically asks which expression represents her gross pay each day, the correct and complete answer (before simplification) is: 35h+567\boxed{\frac{35h + 56}{7}}
This approach aligns with algebraic principles of expressions, especially distributing division across addition, and helps reinforce understanding of variables, coefficients, and simplifying expressions.