How many did they each send?

Question

Karen,Jim,and Michael sent a total of 94 messages over their cell phones during the weeken. Karen sent 8 more messages than Jim. Michael sent 4 time as many messages as Karen. How many messages did they each send?

Answer 1

Let J be the number of messages Jim sent

Then K is the number of messages Karen sent.

K = J + 8

Michael (M) = 4*K

so J + K + M = 94

so J + (J+8) + 4(J+8) = 94

6J + 40 = 94

6J = 54

J = 9

So, Jim sent 9 messages, Karen sent 17 messages, Michael sent 68 messages

Check:

9+17+68=94

Answer 2

 

  K + J + M = 94

 

K = J+8 --> J = K-8

 

M = 4K

 

Substitution:

 K + K-8 + 4K = 94

6K - 8 = 94

6K = 102

K = 17

 

Karen sent 17

Michael sent 68

Jim sent 9