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 :
The problem states that Harriet earns the same amount of money each day, and her total gross pay at the end of 7 workdays is represented as $35h + 56$ dollars. We are asked to determine the expression that represents her gross pay each day.
Step-by-Step Explanation:
- Understanding the total pay:
Harriet’s total pay after 7 workdays is given as $35h + 56$ dollars. This total pay can be broken down into her daily earnings multiplied by the number of workdays. Since she works 7 days and earns the same amount each day, her daily pay is the same every day. - Define the daily pay:
Let’s define the daily pay as $x$, where $x$ represents the amount of money Harriet earns each day. After 7 days, the total pay would then be expressed as: $$
7x
$$ This is the total amount of money Harriet earns after working 7 days. - Set up an equation:
We are told that her total pay after 7 days is $35h + 56$. Therefore, we can set up the equation: $$
7x = 35h + 56
$$ This equation tells us that Harriet’s total pay for 7 days is equal to $35h + 56$. - Solve for $x$ (her daily pay):
To find the expression for her daily pay, we solve for $x$ by dividing both sides of the equation by 7: $$
x = \frac{35h + 56}{7}
$$ Simplifying the right-hand side: $$
x = \frac{35h}{7} + \frac{56}{7}
$$ $$
x = 5h + 8
$$ - Conclusion:
Harriet’s gross pay each day is represented by the expression $5h + 8$ dollars. This means that for each day she works, Harriet earns $5h + 8$ dollars.
Final Answer:
The expression that represents Harriet’s gross pay each day is $\boxed{5h + 8}$.
This method uses basic algebraic principles to break down the total pay into the daily pay, providing a clear solution to the problem.