We and us and half of us and half of half of us, if you and us, we will be 35 in total.




Let's break down the statement mathematically. 

Let \( x \) represent "us."

1. The phrase "We and us" can be interpreted as \( x + 1 \) (assuming "we" refers to one additional person).
2. "Half of us" is \( \frac{x}{2} \).
3. "Half of half of us" is \( \frac{x}{4} \).
4. "If you and us" can be interpreted as \( x + 1 + 1 = x + 2 \) (including "you" as one more person).

Combining these, the equation becomes:

\[
(x + 1) + \frac{x}{2} + \frac{x}{4} + (x + 2) = 35
\]

Now, let's simplify this equation:

1. Combine the terms:

\[
x + 1 + \frac{x}{2} + \frac{x}{4} + x + 2 = 35
\]
\[
2x + 3 + \frac{x}{2} + \frac{x}{4} = 35
\]

2. Convert all terms to have a common denominator, which is 4:

\[
\frac{8x}{4} + \frac{12}{4} + \frac{2x}{4} + \frac{x}{4} = 35
\]
\[
\frac{8x + 2x + x + 12}{4} = 35
\]
\[
\frac{11x + 12}{4} = 35
\]

3. Multiply both sides by 4:

\[
11x + 12 = 140
\]

4. Subtract 12 from both sides:

\[
11x = 128
\]

5. Finally, divide by 11:

\[
x = \frac{128}{11} \approx 11.64
\]

Since "us" must be a whole number, it seems there's a misunderstanding in the problem. If we assume "us" must be an integer, we could re-evaluate or round \( x \) to a whole number like 11 or 12.

Would you like to clarify any part or go over the steps in more detail? Here are some related questions to consider:

1. How would the total change if we include more people in "us"?
2. What assumptions are we making about the identities of "we," "you," and "us"?
3. Can we explore similar problems with different total values?
4. How does the concept of fractions play into this problem?
5. What would be the implications if "you" represented multiple people?

**Tip:** Always clarify the roles of terms in word problems to set up equations accurately!

We and us and half of us and half of half of us, if you and us, we will be 35 in total.

Explore the step-by-step solution to the word problem involving multiple people and fractions, leading to the equation x + 1 + (x/2) + (x/4) + (x + 2) = 35. This problem emphasizes algebraic concepts and is suitable for students in Grades 6-8.

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