elsa,ryan, and jim sent a total of 116 text messgaes during the weekend. ryan sent 4 times as many messages as jim. elsa sent 10 fewer messages than jim. how many messages did they each send?

The number of messages sent by Elsa, Ryan and Jim are 11 , 84 and 21 respectively.

Explanation

Suppose, the number of messages Jim sent is [tex]x[/tex]

As Ryan sent 4 times as many messages as Jim, so the number of messages sent by Ryan [tex]= 4x[/tex]

Also, Elsa sent 10 fewer messages than Jim, so the number of messages sent by Elsa [tex]= x-10[/tex]

Given that, they sent a total of 116 text messages. So the equation will be.......

[tex]x+4x+(x-10)=116\\ \\ 6x-10=116\\ \\ 6x= 126\\ \\ x= \frac{126}{6}= 21[/tex]

So, the number of messages sent by each of them.....

[tex]Jim = 21\\ Ryan = 4*21= 84\\ Elsa= 21-10= 11[/tex]