Question

Jaxon had 3 times as much money as Camila. After Jaxon gave $285 to Camila, he had twice as much money as she did. How much money did Jaxon have at first?

Answer 1

Let \( J \) be the amount of money Jaxon had initially, and \( C \) be the amount of money Camila had initially.

From the problem, we know:

1. \( J = 3C \) (Jaxon has 3 times as much money as Camila).
2. After Jaxon gave $285 to Camila, he had twice as much as she did.

After Jaxon gives $285 to Camila, his amount will be \( J - 285 \) and Camila's amount will be \( C + 285 \). According to the problem:

\[
J - 285 = 2(C + 285)
\]

Now we will substitute \( J \) from the first equation into the second equation. Replacing \( J \) with \( 3C \):

\[
3C - 285 = 2(C + 285)
\]

Distribute the 2 on the right side:

\[
3C - 285 = 2C + 570
\]

Now, subtract \( 2C \) from both sides:

\[
3C - 2C - 285 = 570
\]
\[
C - 285 = 570
\]

Now add 285 to both sides to solve for \( C \):

\[
C = 570 + 285
\]
\[
C = 855
\]

Now that we have \( C \), we can find \( J \) using the first equation \( J = 3C \):

\[
J = 3 \times 855 = 2565
\]

Thus, Jaxon initially had \(\boxed{2565}\) dollars.

To verify:
- If \( C = 855 \), then \( J = 3C = 2565 \).
- After giving $285 to Camila, Jaxon has \( 2565 - 285 = 2280 \), and Camila has \( 855 + 285 = 1140 \).
- Check the condition: \( 2 \times 1140 = 2280\), which holds true.

Therefore, Jaxon's initial amount of money is confirmed as \(\boxed{2565}\).