misssleepingwit
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# 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

The answer is 32 years old. We have 6 people with ages a, b, c, d, e, f We want to calculate d (the age of the 4th person) It is given: Their average age is 27: $\frac{a+b+c+d+e+f}{6} =27$                                           ⇒ a + b + c + d + e + f = 27 × 6 = 162 The average age of the first four people: $\frac{a+b+c+d}{4} =23$                                                                       ⇒ a + b + c + d = 23 × 4 = 92 he average age of the last three people: $\frac{d+e+f}{3} =34$                                                                       ⇒ d + e + f = 34 × 3 = 102 a + b + c + d + e + f = 162 a + b + c + d = 92 92 + e + f = 162 e + f = 162 - 92 = 70 d + e + f = 102 e + f = 70 d + 70 = 102 d = 102 - 70 = 32