How many messages did they each send?

Question

Rain, Ahmad and Eric sent a total of 66 messages over their phone. Ahmad sent 6 more messages than Rain. Eric sent 2 times as many messages as Ahma.

Answer 1

r + a + e = 66   EQUATION 1

 

a = r + 6     EQUATION 2

 

e = 2a 

 

e = 2(r + 6)   substitute for a

  

e = 2r + 12     EQUATION 3

 

now substitue EQUATION 2  and  EQUATION 3 back into EQUATION 1

 

 r +(r + 6) + (2r + 12) = 66

 

4r + 18 = 66

 

4r = 48

 

r = 12      Rain sent 12 messages

 

a = 6 + 12  using EQUATION 2

 

a = 18   Ahmad sent 18 messages

 

e = 2(a) 

 

e = 36  Eric sent 36 messages

 

 

Check:

 

12 + 18 + 36 = 66