SOLUTION: The average age of three girls is seventeen years four months. The average age of two of them is seventeen years three months. How old is the third girl?

Question 1124502: The average age of three girls is seventeen years four months. The average age of two of them is seventeen years three months. How old is the third girl?
Found 2 solutions by ankor@dixie-net.com, greenestamps:
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
let the 3 girls' ages be a, b, c
Change the average ages to months: 12(17) + 4 = 208 months & 207 months
:
The average age of three girls is seventeen years four months.
= 208
a + b + c = 208*3
a + b + c = 624
The average age of two of them is seventeen years three months.
= 207
a + b = 207*2
a + b = 414
How old is the third girl? (c)
Use elimination with these two simplified equations
a + b + c = 624
a + b + 0 = 414
------------------subtraction eliminates a & b, find c
0 + 0 + c = 210 months
210/12 = 17.5, c is 17 yrs 6 months
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The solution by the other tutor using formal algebra is of course valid. However, for problems like this involving averages of numbers that are close together, logical reasoning gets you to the answer much faster.

If the average age of all three is 17 years 4 months, and the average age of two of the three is 17 years 3 months, then on average each of those two ages is 1 month below the average for all three. To balance those two ages that are 1 month UNDER the average for all three, the age of the third must be 2 months OVER the average for all three.

17 year 4 months, plus 2 months, equals 17 years 6 months.
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