Six people are standing in line for concert tickets. their average age is 27. the average age of the first four people in line is 23. the average age of the last three people is 34. how old is the fourth person in line?

Total age 
6 * 27 
162 

Subtotal age of first 4 
4 * 23 
92 

Subtotal of last 3 
3 * 34 
102 

In the total of the first 4 and last 3 
the 4th person has been counted twice. 
This second time must be subtracted. 

Therefor 
92 + 102 - x = 162 
194 - x = 162 

Subtract 194 from both sides 
-x = -32 

Multiply both sides by -1 
x = 32 

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The linear equation is: y=ax+b