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 and E xplanation is:
To find Harriet’s gross pay each day, we are given that her total gross pay for 7 workdays is:
$$
35h + 56 \text{ dollars}
$$
Step 1: Understand What We’re Solving
We want to find how much Harriet earns in one day, given that her total for 7 days is $35h + 56$. Since she earns the same amount each day, we can divide the total by 7.
Step 2: Divide the Expression by 7
We divide the entire expression $35h + 56$ by 7:
$$
\frac{35h + 56}{7}
$$
To simplify:
- Divide each term in the numerator by 7: $$
\frac{35h}{7} + \frac{56}{7} = 5h + 8
$$
✅ Final Answer:
$$
\boxed{5h + 8}
$$
📘 Explanation (300+ Words):
This is an algebraic problem involving division of a polynomial by a constant. We’re told that Harriet earns a fixed amount of money each day, and her total pay for 7 days is represented by the expression $35h + 56$. The goal is to find her daily earnings, which involves finding an expression that, when multiplied by 7, gives $35h + 56$.
To do this, we apply the distributive property of division over addition. This property allows us to divide each term in a sum separately. So instead of trying to simplify the entire expression at once, we break it down:
$$
\frac{35h + 56}{7} = \frac{35h}{7} + \frac{56}{7}
$$
- First, divide $35h$ by 7: $$
\frac{35h}{7} = 5h
$$ - Next, divide 56 by 7: $$
\frac{56}{7} = 8
$$
Now, combine the two results:
$$
5h + 8
$$
This simplified expression tells us that each day, Harriet earns an amount equal to 5 times some hourly rate $h$, plus 8 extra dollars. This could represent, for example, a base fee or bonus included daily.
Using algebra in this way helps break down complex earnings over multiple days into a simple, manageable form. This is useful for budgeting, payroll, and understanding financial patterns.