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 are told that:
- Her total gross pay for 7 days is represented by the expression: 35h+5635h + 56
- Since she earns the same amount each day, we divide the total expression by 7 to find her daily pay.
Step-by-step:
Daily pay=35h+567\text{Daily pay} = \frac{35h + 56}{7}
Now divide each term in the numerator by 7: =35h7+567= \frac{35h}{7} + \frac{56}{7} =5h+8= 5h + 8
✅ Correct Answer:
5h+8\boxed{5h + 8}
💬 Explanation (300+ words):
This problem is a good example of how to use algebraic expressions and the distributive property to solve real-world problems involving money and consistent pay rates. Harriet earns the same amount each day, which implies her daily pay is constant. Her total pay after 7 days is given by the expression 35h+5635h + 56, where hh is likely a variable tied to her hourly rate, hours worked, or some other factor that affects her pay.
To find out how much she earns each day, we need to divide the total pay by 7, the number of days she worked. This method is based on the concept of equally distributing a quantity over a number of units—in this case, dollars over days.
When dividing a polynomial by a constant, you divide each term in the expression separately. So, 35h35h divided by 7 becomes 5h5h, and 56 divided by 7 becomes 8. This gives us a simplified algebraic expression for Harriet’s gross daily pay: 5h+85h + 8
This result means that each day, Harriet earns an amount that depends on both a variable component (5h5h) and a fixed amount ($8). This could reflect a payment structure where she earns $5 per hour (if hh is hours worked) plus a fixed bonus or allowance of $8 per day.
Understanding how to manipulate and simplify algebraic expressions is crucial for solving real-world problems, especially in finance, budgeting, and payroll calculations.