Answer :
Let's define the number of messages Josh sent as \( J \). According to the problem:
- Elsa sent 10 more messages than Josh, so Elsa sent \( J + 10 \).
- Greg sent 4 times as many messages as Josh, so Greg sent \( 4J \).
The total number of messages sent by all three is 148. Therefore, we can write the equation:
\[ J + (J + 10) + 4J = 148 \]
Combining like terms, we get:
\[ 6J + 10 = 148 \]
Subtracting 10 from both sides gives us:
\[ 6J = 138 \]
Dividing both sides by 6 gives us the number of messages Josh sent:
\[ J = 23 \]
Now we can find out how many messages Elsa and Greg sent:
- Elsa sent \( J + 10 = 23 + 10 = 33 \) messages.
- Greg sent \( 4J = 4 \times 23 = 92 \) messages.
So, Josh sent **23** messages, Elsa sent **33** messages, and Greg sent **92** messages.
- Elsa sent 10 more messages than Josh, so Elsa sent \( J + 10 \).
- Greg sent 4 times as many messages as Josh, so Greg sent \( 4J \).
The total number of messages sent by all three is 148. Therefore, we can write the equation:
\[ J + (J + 10) + 4J = 148 \]
Combining like terms, we get:
\[ 6J + 10 = 148 \]
Subtracting 10 from both sides gives us:
\[ 6J = 138 \]
Dividing both sides by 6 gives us the number of messages Josh sent:
\[ J = 23 \]
Now we can find out how many messages Elsa and Greg sent:
- Elsa sent \( J + 10 = 23 + 10 = 33 \) messages.
- Greg sent \( 4J = 4 \times 23 = 92 \) messages.
So, Josh sent **23** messages, Elsa sent **33** messages, and Greg sent **92** messages.
