word question... please help

Question

carmen juan and rebuben sent a total of 140 messages, Juan sent 8 fewer messages than carmen Ruben sent 2 teims as many messages are Juan. How many messages did each send

Answer 1

Hi, Nykeemah.

 

We will let Carmen's number of messages be c.

If Juan sent 8 fewer than Carmen, he sent c - 8 messages.

Since Ruben sent 2 times as many as Juan, he sent 2(c-8) or 2c - 16 messages.

 

The sum of them all equals 140. That is...

c + (c - 8) + (2c - 16) = 140

 

Let's solve for c:

c + (c - 8) + (2c - 16) = 140

c + c - 8 + 2c - 16 = 140

4c - 24 = 140

4c - 24 + 24 = 140 + 24

4c = 164

c = 164/4 = 41

 

So, Carmen sent 41 messages.

Juan sent 8 fewer, so he sent 41 - 8 or 33 messages.

Ruben sent twice as many as Juan, so he sent 2*33 or 66 messages.

 

Then to check,

 

41 + 33 + 66 = 74 + 66 = 140