Question

Lisa, 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 sentXS?Number of text messages Juan sent00DNumber of text messages Kareem sent:

Answer 1

Let's say that L represents the text messages sent by Lisa, J by Juan and K by Kareem.

in this way, we have the following equations

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

Now, let's solve the equations system

1. substitute l = j-5 and simplify

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

2. substitute k=3j and simplify

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

- We have found that Juan has sent 21 text messages

3. for K=3J substitute J=21

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

- we found that Kareem has sent 63 text messages

4. for L=J-5 substitute J=21

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

- Thus, Lisa sent 16 text messages

In conclusion, the solution to the system of equations is the following:

J = 21, K = 63, L = 16