Math word problem

Question

3 TV networks gathered an average of 29.4 million views. Network 1 has 1.4 million more than network 2 and network 3 has 1.4 million less than network 2 how many views did each hve?

Answer 1

There is a quick short solution but I am showing the long solution:   where M = million viewers

 

1)  NW1 = 1.4 M + NW2

2)  NW3 = NW2 - 1.4 M

 

NWavg = (NW1 + NW2 + NW3)/3 = 29.4 M

 

rearranging, 3)  NW1 + NW2 + NW3 = 29.4 M x 3  

 

3 equations and 3 unknowns

 

Now substitute 1) and 2) into 3) and solve for NW2:

(1.4 M + NW2) + NW2  + (NW2 - 1.4 M) = 29.4 M x 3

3*NW2 = 3*29.4 M (3's cancel)

 

NW2 = 29.4 M

NW1 = 29.4 M + 1.4 M  = 30.8 M

NW3  = 29.4 M - 1.4 M  = 28.0 M

 

Note only NW1 and NW3 differed from NW2 by the same difference but with diffrtent signs