Question

mai, rafael, and hong sent a total of 106 text messages over their cell phones during the weekend. rafael sent 8 more messages than mai. hong sent 4 times as many messages as rafael. how many messages did they each send?
number of text messages mai sent:
number of text messages rafael sent:
number of text messages hong sent:

Explanation:

Step1: Define variables

Let the number of text messages Mai sent be $x$. Then Rafael sent $x + 8$ messages, and Hong sent $4(x + 8)$ messages.

Step2: Set up equation

The total number of messages is 106, so $x+(x + 8)+4(x + 8)=106$.

Step3: Simplify equation

First, expand the terms: $x+x + 8+4x+32 = 106$. Then combine like terms: $6x+40 = 106$.

Step4: Solve for x

Subtract 40 from both sides: $6x=106 - 40=66$. Then divide by 6: $x=\frac{66}{6}=11$.

Step5: Find messages for each

• Mai: $x = 11$
• Rafael: $x + 8=11 + 8 = 19$
• Hong: $4(x + 8)=4\times19 = 76$

Answer:

Mai sent 11 messages, Rafael sent 19 messages, Hong sent 76 messages.