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Same prize as last weekend for whoever gets this first (either on the blog, or on Facebook; you’re competing against each other here). Any $5 album from Amazon.com. Ready?
A small town has 3 theaters in it. Last Saturday night, the average age in the first theater was 29, and the average age in the second theater was 24. If the overall average theatergoer on that night was 36 years old and the ratio of attendees for the three theaters was 2:3:10, respectively, then what was the average age of the attendees in the third theater?
Good luck, folks. I’ll post the answer and contact the winner (if there is one) on Monday. Remember: you can’t win if I can’t contact you.
UPDATE: Congrats to Codi, who nailed it on Facebook. Answer below the cut.
This is an average question, so let’s use the average table! Start by filling in what the questions tells us (and plugging in obvious values for numbers of people in the theaters based on the given ratio):
|
2 people
(1st theater) |
29 years per person
|
|
|
3 people
(2nd theater) |
24 years per person | |
|
10 people
(3rd theater) |
||
|
15 people
(all theaters) |
36 years per person |
Now fill in the sums:
|
2 people
(1st theater)
|
29 years per person
|
58 years
|
|
3 people
(2nd theater)
|
24 years per person
|
72 years
|
|
10 people
(3rd theater)
|
||
|
15 people
(all theaters)
|
36 years per person
|
540 years
|
Hopefully you see that the sum of the ages in the first and second theaters is 58+72=130. Therefore, in order for the sum of everyone’s ages to be 540, the sum of the ages of the people in the third theater has to be 540-130=410. If there are 10 people in a room whose ages add up to 410, the average age in the room has to be 41! To finish the table:
|
2 people
(1st theater)
|
29 years per person
|
58 years
|
|
3 people
(2nd theater)
|
24 years per person
|
72 years
|
|
10 people
(3rd theater)
|
41 years per person
|
410 years
|
|
15 people
(all theaters)
|
36 years per person
|
540 years
|
Note that the average table allows you to check your work to make sure you didn’t make any mistakes. In the left-hand column 2+3+10=15, and in the right-hand column 58+72+410=540. That’s a beautiful thing. I literally weep when I see it.