Question

Charmaine, Dante, and Rafael sent a total of 77 text messages over their cell phones during the weekend. Charmaine sent 9 fewer messages than Dante. Rafaelsent 2 times as many messages as Charmaine. How many messages did they each send?Number of text messages Charmaine sent:Number of text messages Dante sent:Number of text messages Rafael sent:

Answer 1

Let x be the number of messages Dante sent.

We know that Charmaine sent 9 fewer messages than Dante this means that Dante sent:

`x-9`

messages.

We also know that Rafael sent 2 times as many messages as Charmaine, then Rafael sent:

`2(x-9)`

messages.

Now that we have an expression for the messages each of them sent we add them and equate the sum to 77, the total number of text. Hence we have the equation:

`x+x-9+2(x-9)=77`

Solving for x we have:

`\begin{gathered} x+x-9+2(x-9)=77 \\ 2x-9+2x-18=77 \\ 4x-27=77 \\ 4x=77+27 \\ 4x=104 \\ x=(104)/(4) \\ x=26 \end{gathered}`

Now that we have the value of x, we plug it in each of the expressions for the number of messages each one of them sent and we conclude that:

Charmaine sent 17 messages.

Dante sent 26 messages.

Rafael sent 34 messages.