SOLUTION: 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

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Question 1046545: 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?
Found 3 solutions by solver91311, ikleyn, MathTherapy:
Answer by solver91311(24713)   (Show Source):
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If the average of numbers is , then the sum of the numbers must be .

The sum of the ages of all 6 people is then 6 times 27 or 162.

The sum of the ages of the first 4 people is 4 times 23 or 92.

So the sum of the ages of the last 2 people must be 162 minus 92 or 70.

Since the sum of the ages of the last three must be 3 times 34 or 92, the age of the 4th person has to be 92 minus 70, or 22.

John

My calculator said it, I believe it, that settles it

Answer by ikleyn(52877)   (Show Source):
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Answer by MathTherapy(10556)   (Show Source):
You can put this solution on YOUR website!
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?

Let the age of the 4th person be F
Sum of the 1st four in line: 4(23), or 92
Sum of 1st 3: 92 - F (excludes the 4th person's age)
Sum of the last 3 in line: 3(34), or 102
Sum of last 2: 102 - F (excludes the 4th person's age)
Sum of all 6: 6(27), or 162 (INCLUDES 4th person's age)
We now get: F + 92 - F + 102- F = 162
- F + 194 = 162
- F = 162 - 194
- F = - 32
F, or 4th person's age = , or