Antonio and Abby had the same number of paperclips. After Antonio gave 30 paperclips to Abby, Abby had twice as many paperclips as Antonio. How many paperclips did they have in all?

Let's solve this problem step by step.

### Step 1: Define variables
Let the number of paperclips each had initially be \( x \).

- Antonio had \( x \) paperclips.
- Abby also had \( x \) paperclips.

After Antonio gave 30 paperclips to Abby:
- Antonio had \( x - 30 \) paperclips.
- Abby had \( x + 30 \) paperclips.

### Step 2: Set up an equation based on the problem condition
The problem says that after the transfer, Abby had twice as many paperclips as Antonio. So, we can write the equation:
\[
x + 30 = 2(x - 30)
\]
This equation represents the fact that Abby's paperclips are double Antonio's after the transfer.

### Step 3: Solve the equation
Now, solve for \( x \).

1. Expand the equation:
\[
x + 30 = 2x - 60
\]
2. Subtract \( x \) from both sides:
\[
30 = x - 60
\]
3. Add 60 to both sides:
\[
90 = x
\]

So, Antonio and Abby initially had 90 paperclips each.

### Step 4: Find the total number of paperclips
Since they both had 90 paperclips each initially, the total number of paperclips they had in all is:
\[
90 + 90 = 180
\]

Thus, Antonio and Abby had **180 paperclips in total**.

Would you like further details, or do you have any questions?

Here are some related questions you might find helpful:
1. What if Antonio gave 40 paperclips instead of 30? How would that change the result?
2. How would the situation change if Abby gave paperclips to Antonio instead?
3. If Antonio had 50 fewer paperclips than Abby, how many would each have?
4. What if the number of paperclips they had initially were different?
5. How can we solve similar problems using different methods?

**Tip:** When dealing with word problems, defining variables clearly and translating words into mathematical equations is crucial for solving the problem accurately.

Discover how to solve a linear equation word problem where Antonio gives 30 paperclips to Abby, and Abby ends up with twice as many as Antonio. This problem explains step-by-step how to set up the equation and find the total number of paperclips. Suitable for Grades 6-8.

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