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 daily gross pay, we are given her total gross pay after 7 workdays as:
Total gross pay: 35h + 56 dollars
Since Harriet earns the same amount each day, we can find her daily pay by dividing the total pay by 7: Daily pay=35h+567\text{Daily pay} = \frac{35h + 56}{7}
Now, divide each term in the numerator by 7: 35h7+567=5h+8\frac{35h}{7} + \frac{56}{7} = 5h + 8
✅ Correct answer: 5h + 8
🧠 Explanation (300 words):
This problem involves algebraic expressions and the concept of evenly distributing a total amount over a number of units—in this case, the total earnings over 7 workdays. The total amount Harriet earned over 7 days is given as 35h + 56 dollars. This expression tells us that her pay includes a variable component (likely based on hours worked, represented by h) and a fixed component of 56 dollars.
Since Harriet earns the same amount every day, we can assume that her daily pay multiplied by 7 gives the total expression. To find the amount she earns in one day, we simply need to divide the total expression by 7, just as you would divide a total number evenly among a group.
We apply the distributive property of division over addition: 35h+567=35h7+567\frac{35h + 56}{7} = \frac{35h}{7} + \frac{56}{7}
Next, we simplify each term:
- 35h7=5h\frac{35h}{7} = 5h
- 567=8\frac{56}{7} = 8
So the simplified expression becomes 5h + 8, which means each day Harriet earns 5h dollars based on hours worked, plus an additional $8—possibly representing a fixed daily allowance or bonus.
This method helps break down complex expressions into understandable parts and shows how algebra helps solve real-world problems like pay and time.