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 given:
- Her total gross pay for 7 workdays is: 35h+56 dollars35h + 56 \text{ dollars}35h+56 dollars
We need to find how much she earns each day, assuming it is the same amount daily.
Step 1: Divide Total Gross Pay by Number of Days
Since Harriet works 7 days, and earns the same amount each day, we divide her total pay by 7: 35h+567\frac{35h + 56}{7}735h+56
Step 2: Simplify the Expression
Now simplify the expression:
Break the numerator into two terms: 35h7+567\frac{35h}{7} + \frac{56}{7}735h+756 =5h+8= 5h + 8=5h+8
✅ Correct Answer:
5h+8\boxed{5h + 8}5h+8
📘 Explanation (300+ words):
In algebra, when an expression like 35h + 56 represents a total over multiple parts (in this case, 7 days), you can find the value for one part (each day) by dividing the total by the number of parts (7).
Harriet’s gross pay after 7 days is 35h + 56, where:
- 35h likely represents an hourly wage or a variable based on time or hours.
- 56 is likely a fixed component, such as a bonus or base pay.
To find her daily pay, we divide this entire expression by 7. This is known as applying the distributive property of division over addition: a+bc=ac+bc\frac{a + b}{c} = \frac{a}{c} + \frac{b}{c}ca+b=ca+cb
So, we divide:
- 35h ÷ 7 = 5h, and
- 56 ÷ 7 = 8
Adding those gives us 5h + 8, which means Harriet earns a variable component of 5h and a fixed component of 8 dollars each day.
This expression tells us that Harriet’s daily earnings are influenced by a changing factor (like hours worked, represented by h), and a consistent amount (perhaps a daily allowance or bonus), represented by 8 dollars.
This approach demonstrates how expressions in algebra can model real-world earnings and how division helps break down totals into per-unit amounts—an important skill in both math and financial literacy