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 out how much Harriet earns per day, let’s break down the problem step by step.
Step 1: Understand the total pay
We know that Harriet’s total gross pay at the end of 7 workdays is given by the expression:
[
35h + 56
]
This is the total amount Harriet earns for 7 workdays.
Step 2: Define the unknown
Let the amount Harriet earns each day be represented by ( x ). If she works for 7 days, her total pay is simply her daily pay multiplied by the number of days she worked. Therefore, her total pay for 7 days is:
[
7x
]
This represents the total amount Harriet earns in 7 days.
Step 3: Set up the equation
Now, we know that Harriet’s total gross pay after 7 workdays is ( 35h + 56 ). So, we can equate this expression to the total pay for 7 days:
[
7x = 35h + 56
]
Step 4: Solve for ( x )
To find out how much Harriet earns per day, we need to solve for ( x ). To do that, divide both sides of the equation by 7:
[
x = \frac{35h + 56}{7}
]
Now, simplify the right-hand side:
[
x = \frac{35h}{7} + \frac{56}{7}
]
[
x = 5h + 8
]
Conclusion
Thus, the expression that represents Harriet’s gross pay each day is:
[
5h + 8
]
Explanation
- The key is recognizing that the total pay for 7 days is equal to the daily pay multiplied by 7.
- By setting up the equation ( 7x = 35h + 56 ), we can solve for ( x ), which represents the amount Harriet earns each day.
- Dividing the total expression by 7 gives us the simplified daily pay formula: ( 5h + 8 ).
This method is based on simple algebraic manipulation, using the total pay and the number of workdays to express the daily wage.