Question

Yoko, Austin, and Tom sent a total of 96 text messages over their cell phones during the weekend. Tom sent 3 times as many messages as Austin. Austin sent 6 fewer messages than Yoko. How many messages did they each send? Number of text messages Yoko sent: Number of text messages Austin sent: Number of text messages Tom sent:

Answer 1

Solution

Given that:

Total number of messages sent is 96

Let the number of messages Yoko sent be x

=> Austin will send x - 6 (since austin sent 6 fewer messages)

=> Tom will send 3(x - 6) (since Tom sent 3 times as many messages)

Since they make a total of 96

$\begin{gathered} \Rightarrow x+x-6+3(x-6)=96 \\ \\ \Rightarrow x+x-6+3x-18=96 \\ \\ \Rightarrow5x-24=96 \\ \\ \Rightarrow5x=96+24 \\ \\ \Rightarrow5x=120 \\ \\ \Rightarrow x=\frac{120}{5} \\ \\ \Rightarrow x=24 \end{gathered}$

Hence, Yoko sent: 24 messages

Austin sent: 24 - 6 = 18 messages

Tom sent: 3(18) = 54 messanges

Number of text messages Yoko sent: 24 messages

Number of text messages Austin sent: 18 messages

Number of text messages Tom sent:​ 54 messanges