father`s age is 3 times the sum of ages of his 2 children .after 5 yrs his age will be twice the sum of ages of the two children . find the present age of father
4 years, 4 months ago
Let the children's ages be \( x \) and \( y \) and the father's age \( z \). So \( z=3(x+y) \) and \( z+5=2(x+y+10)\).
Then we get \( z=2x+2y+15 \).Then we can substitute \( z=3(x+y) \) which is \( z=3x+3y \).So \( x+y=15\),and \( z=45 \)
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Let \(c\) be the sum of the 2 children's age and \(f\) be the father's age
Simplifying (2): \(5+f=2c+20\Rightarrow f=2c+15\)
Combining (1) and (2): \(3c=2c+15\). Therefore, we could get \(c=15\)
From (1): \(f=3c\), we could get the father's age: \(f=3(15)\Rightarrow f=45\)
Therefore, the father's present age is 45 years old.