Question

Usa, Juan, and Kareem sent a total of 100 text messages during the weekend. Kareem sent 3 times as many messages as Juan. Lisa sent 5 fewer messagesthan Juan. How many messages did they each send?Number of text messages Usa sent:0X52Number of text messages Juan sent:Number of text messages Kareem sent:0

Answer 1

Let's assume the following:

L - indicates the number of text messages sent by Lisa

J - by Juan, and

K - by Kareem

Having said that, we propose the following equations

`\begin{gathered} L+J+K=100 \\ K=3\cdot J \\ L=J-5 \end{gathered}`

Now, let's solve this system of equations

1. from L=J-5, then

`\begin{gathered} J-5+J+K=100 \\ 2J+K-5=100 \\ \end{gathered}`

2. from K=3J, then

`\begin{gathered} 2J+3J-5=100 \\ 5J-5=100 \\ 5J=100+5 \\ J=(105)/(5) \\ J=21 \end{gathered}`

- we can see that Juan sent 21 text messages

3. substitute J=21 in L=J-5

`\begin{gathered} L=21-5 \\ L=16 \end{gathered}`

- thus, Lisa sent 16 text messages

4. substitute J=21 in K=3J

`\begin{gathered} K=3\cdot21 \\ K=63 \end{gathered}`

- therefore, Kareem sent 63 text messages

In conclusion, they sent the following number of messages

Lisa: 16

Juan: 21

Kareem: 63