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:
Correct Answer:
The expression that represents Harriet’s gross pay each day is:
35h+567\frac{35h + 56}{7}
Explanation
To find Harriet’s daily gross pay, we start with the information that she earns the same amount each day and that her total gross pay over 7 days is given by the expression 35h + 56. The phrase “gross pay at the end of 7 workdays” tells us that the expression 35h + 56 is her total earnings after working for 7 days.
When you want to determine the amount someone earns per day, and you know their total earnings and the number of days worked, you divide the total earnings by the number of days. Mathematically, this is written as: Daily pay=Total pay over 7 days7\text{Daily pay} = \frac{\text{Total pay over 7 days}}{7}
Plug in the expression for total pay: Daily pay=35h+567\text{Daily pay} = \frac{35h + 56}{7}
This is a valid algebraic expression representing her daily gross pay.
Let’s break down the expression further to better understand it. Using the distributive property of division over addition, we can simplify: 35h+567=35h7+567=5h+8\frac{35h + 56}{7} = \frac{35h}{7} + \frac{56}{7} = 5h + 8
So, 5h + 8 is the simplified form of Harriet’s daily gross pay.
This means that each day, Harriet earns an amount equal to 5 times h, plus 8 dollars. This could represent, for example, a situation where Harriet earns $5 per hour (where “h” is the number of hours worked each day), plus an $8 daily bonus.
But since the question specifically asks for the expression representing her gross pay each day—not necessarily its simplified form—the best direct answer is: 35h+567\boxed{\frac{35h + 56}{7}}
This format shows the logic of dividing total earnings by the number of days, which is key to understanding the situation.
