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 how much Harriet earns each day, we are given:
- Her total gross pay for 7 days is: 35h+5635h + 56
Since she earns the same amount each day, we divide her total pay by 7 to find her daily pay:
Step 1: Divide the total gross pay by 7
35h+567\frac{35h + 56}{7}
Step 2: Use distributive property to simplify
We divide each term in the numerator by 7: =35h7+567= \frac{35h}{7} + \frac{56}{7} =5h+8= 5h + 8
✅ Correct answer: 5h+8\boxed{5h + 8}
📘 Explanation (300+ words)
This problem involves algebraic expressions and division of polynomials. Harriet’s total gross pay over 7 workdays is given as an algebraic expression: 35h+5635h + 56. This means that her total pay is made up of two parts: a variable part (35h35h) and a constant part (56). The variable part likely depends on hours worked or a rate associated with a variable “h”.
Since Harriet earns the same amount each day, we are asked to find how much she earns per day. To find this, we must divide the total amount she earned over the 7 days by 7. In algebra, this is written as: 35h+567\frac{35h + 56}{7}
When dividing an algebraic expression by a constant, you divide each term in the expression separately. This uses the distributive property of division over addition. That means: 35h+567=35h7+567\frac{35h + 56}{7} = \frac{35h}{7} + \frac{56}{7}
Now we simplify each term:
- 35h7=5h\frac{35h}{7} = 5h
- 567=8\frac{56}{7} = 8
So, Harriet earns: 5h+85h + 8
each day. This expression tells us that each day, Harriet’s earnings are a combination of a variable part (5h5h) and a fixed amount (88). This type of question helps students practice key algebra skills, such as simplifying expressions and understanding variables in context.