SOLUTION: Four years ago a man was 2 and a 1/2 times as old as his son, but in five years time, he will only be twice as old as his son. How old is the man now?

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Question 1141483: Four years ago a man was 2 and a 1/2 times as old as his son, but in five years time, he will only be twice as old as his son. How old is the man now?
Found 3 solutions by josgarithmetic, MathTherapy, ikleyn:
Answer by josgarithmetic(39615)   (Show Source): You can put this solution on YOUR website!
y, man
n, son







Multiply the future equation by 5;
Multiply the past equation by 2;




:
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!

Four years ago a man was 2 and a 1/2 times as old as his son, but in five years time, he will only be twice as old as his son. How old is the man now?
FYI: The man is NOT 85  years-old as reported by the other person. 

Answer by ikleyn(52769)   (Show Source): You can put this solution on YOUR website!
 .


Let y be the man's age, and
let n be the son's age.


From the condition, you have these two equations


y-4 = ,             (1)
 
y+5 = 2(n+5).               (2)


Simplify, by multiplying equation (1) by 2 (both sides)'


2y-8 = 5n-20,               (1')

y+5 = 2n+10                 (2')


2y-5n = -12,                (3)

y-2n = 5.                   (4)


Multiply equation (3) by 2;
Multiply equation (4) by 5.


4y-10n = -24,               (5)

5y-10n =  25                (6)

 
Subtract equation (5) from equation (6). You will get


5y - 4y = 25 - (-24)

y       = 49


ANSWER.  The man's age is 49 years.


CHECK.   Then from equation(2),  49+5 = 2*(n+5)  ====>  54 = 2*(n+5)  ====>  n+5 = 54/2 = 27  ====>  n = 27-5 = 22.


         Thus the son's age is 22 years, and you can check that the equation (1) is valid, too.  The check is completed.





 

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