the average age of 30 soldiers is 25. The average age of the first 15 of them is 24 and the last 14 of them is 26 years. What is the age of the 16th soldier?

Question

anonymous · Answer

Think about how you find the average of a set of numbers.  First you sum them up, then you divide by the number of elements, right?  

The average age of 30 soldiers is 25, so you have 30 soldiers whose ages added equal 30*25=750.  The sum of the ages of 15 soldiers with avg age 24 is 15*24=360.  The sum of the ages of 14 soldiers aged 26 is 14*26=364.  So the sum of the ages of our 29 soldiers is 360+364=724.  Subtract 750 which is the sum of the ages of all 30 minus 724 to get the age of the last soldier, which is 26.

anonymous · Answer

Thanks so
Much Matt! That makes sense!!