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 gross pay over 7 days by 7. Her total gross pay is given as: 35h+5635h + 56
So, we divide this total by 7: 35h+567\frac{35h + 56}{7}
Now, we simplify this expression by dividing each term in the numerator by 7: 35h7+567=5h+8\frac{35h}{7} + \frac{56}{7} = 5h + 8
✅ Correct answer: 5h+8\boxed{5h + 8}
🧠 Explanation (300+ words):
This is a problem involving algebraic expressions and division of a polynomial by a constant. Harriet earns the same amount each day, which means her daily pay is consistent. If we are given her total gross pay over a number of days, we can find the amount she earns each day by dividing that total by the number of days she worked.
In this case, her total pay over 7 days is given as 35h+5635h + 56. This expression includes a variable term (35h), which could represent hours worked or a rate based on hours, and a constant term (56), which could be a fixed bonus or base amount.
To determine how much she earns each day, we divide this total by 7: 35h+567\frac{35h + 56}{7}
This is known as distributive division in algebra. We apply the division separately to each term:
- Divide 35h35h by 7: 35h7=5h\frac{35h}{7} = 5h
- Divide 5656 by 7: 567=8\frac{56}{7} = 8
Add these two results together: 5h+85h + 8
This final expression represents her daily gross pay. It means Harriet earns 5h dollars plus 8 dollars each day. The variable hh likely stands for a number of hours worked per day or a variable rate of pay. The “+8” suggests a fixed additional amount is added daily.
Understanding how to divide polynomials by constants is an essential skill in algebra, especially for real-life applications like budgeting and payroll.