SOLUTION: Mr. Parabola, a mathematics teacher was traveling by bus with his family consisting of his mother, wife, son and daughter. The bus conductor doubting the son's right to have a half

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Question 814921: Mr. Parabola, a mathematics teacher was traveling by bus with his family consisting of his mother, wife, son and daughter. The bus conductor doubting the son's right to have a half-fare ticket asked, "how old is your daughter?" Mr. Parabola, irritated at having his honesty questioned, confused the conductor with his answer: "My daughter is twice as old as my son. My wife is three times as old as the sum of the ages of my son and daughter, and I am as old as my wife and my daughter. My mother whose age is the total of all our ages is now 69." Can you help the conductor in finding the age of the girl?
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
"My daughter is twice as old as my son. 
D = 2S

My wife is three times as old as the sum of the ages of my son and daughter,
W = 3(S + D)

and I am as old as my wife and my daughter. 
We will let P = Mr. Parabola's age.

P = W + D

My mother whose age is the total of all our ages is now 69."
P + W + S + D = 69

-----------

S we have a system of 4 equations and 4 unknown

D = 2S
W = 3(S + D)
P = W + D
69 = P + W + S + D

Substitute 2S for D in the other three

W = 3(S + 2S)
P = W + 2S
69 = P + W + S + 2S

Simplify
 
W = 3(3S)
P = W + 2S
69 = P + W + 3S

simplify more

W = 9S
P = W + 2S
69 = P + W + 3S

Substitute 9S for W in the other two
equations:

P = 9S + 2S
69 = P + 9S + 3S

Simplify

P = 11S
69 = P + 12S

Substitute 11S for P in the second equation

69 = 11S + 12S

Simplify

69 = 23S
 3 = S 

Substitute 3 for S in

69 = P + 12S
69 = P + 12(3)
69 = P + 36
33 = P

Substitute 3 for S in

W = 9S
W = 9(3)
W = 27

Substitute 3 for S in

D = 2S
D = 2(3)
D = 6

So the daughter is 6.

Edwin
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