Sen and his three daughters

Algebra Level pending

Sen has three daughters Wen, Fen, and Hen. Three years ago when Sen was twice as old as Hen, he was 30 30 years older than Fen. Now, he is 47 47 years older than Wen. In 4 4 years, Wen will be half as old as Hen. What is the sum of the current ages of Sen and his three daughters?

156 144 170 138 145

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1 solution

Hana Wehbi
Aug 2, 2017

We can solve this with 4 4 equations and 4 4 unknowns.

Let S S stands for age of Sen,

H H stands for age of Hen,

W W stands for age of Wen,

and F F stands for age of Fen, then:

S 3 = 2 ( H 3 ) 1 e q S-3 = 2(H-3)\dots 1eq

S 3 = ( F 3 ) + 30 2 e q S-3 = (F-3)+30\dots 2eq

S = W + 47 3 e q S= W+47\dots 3eq

( W + 4 ) = H + 4 2 4 e q (W+4)= \frac{H+4}{2}\dots 4eq

Solving for our variables yields:

W = 14 , S = 61 , H = 32 , a n d F = 31 W + S + H + F = 138 \implies W=14, S=61, H=32, and \ F=31\implies W+S+H+F= \boxed{138}

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