Question 772387
When Katy was 12, her father was three times her age. Now he is twice her age. How old is Katy now?
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Let Katy's age now = K
Let the Father's age now be F
Let x = the number of years ago it was when her father was 3 times her age.
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When Katy was 12,
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That was x years ago so
 
K - x = 12
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her father was three times her age.
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That was x years ago, so

F - x = 3(K - x)
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Now he is twice her age
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F = 2K

So we have this system of three equations:


K - x = 12
F - x = 3(K - x)
F = 2K

Simplifying them and putting the system in standard order

  K       -  x = 12
-3K +  F  + 2x =  0
-2K +  F       =  0

Solve that by elimination or substitution and get

K=24, F=48, x=12

Answer: Katy is 24, her father is 48, (48 is twice her age 24, that checks)
12 years ago Katy was 12 and her father was 36  (36 is 3 times 12,
that checks).

Edwin</pre>