https://r2.erweima.ai/mathbot/image/1726351244203in6hj230.jpg

The problem described in the image is as follows:

- Emilia, Nicolás, and Juan José sent a total of 127 text messages during the weekend.
- Juan José sent 3 times the number of messages that Emilia sent.
- Emilia sent 7 messages fewer than Nicolás.

We are asked to determine how many messages each person sent.

### Let:
- \( E \) be the number of messages Emilia sent.
- \( N \) be the number of messages Nicolás sent.
- \( J \) be the number of messages Juan José sent.

### According to the problem, we can write the following equations:
1. \( E + N + J = 127 \) (the total number of messages sent is 127).
2. \( J = 3E \) (Juan José sent 3 times as many messages as Emilia).
3. \( N = E + 7 \) (Nicolás sent 7 more messages than Emilia).

### Substituting equations 2 and 3 into equation 1:

\[
E + (E + 7) + 3E = 127
\]

### Simplifying the equation:

\[
5E + 7 = 127
\]

\[
5E = 120
\]

\[
E = 24
\]

### Now that we know \( E = 24 \), we can find the number of messages sent by Nicolás and Juan José:

- \( N = E + 7 = 24 + 7 = 31 \)
- \( J = 3E = 3 \times 24 = 72 \)

### Therefore:
- Emilia sent 24 messages.
- Nicolás sent 31 messages.
- Juan José sent 72 messages.

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

Here are 5 related questions to consider:
1. If Juan José had sent twice the number of messages as Emilia, how would the solution change?
2. What if Nicolás had sent 10 messages more than Emilia instead of 7?
3. How would the total number of messages change if the total was 150 instead of 127?
4. Can you write a similar problem involving four people and different relationships between their messages?
5. If Emilia had sent half the number of messages Nicolás sent, how would the equations be different?

**Tip:** When solving systems of equations, substituting variables is often a key step in reducing complexity!

Emilia, Nicolás y Juan José enviaron un total de 127 mensajes de texto durante el fin de semana. Juan José envió 3 veces el número de mensajes que envió Emilia. Emilia envió 7 mensajes menos que Nicolás. ¿Cuántos mensajes envió cada uno?

Learn how to solve a system of equations involving Emilia, Nicolás, and Juan José, who sent a total of 127 text messages. Juan José sent 3 times as many as Emilia, and Nicolás sent 7 more than Emilia. This problem explores algebraic concepts for students in Grades 6-8.

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