SOLUTION: A man refused to tell anyone his age,but he likes to drop hints about it. He then remarks that twice his mother's age add up to 140 and also that his age plus his father's age add

Question 386965: A man refused to tell anyone his age,but he likes to drop hints about it. He then remarks that twice his mother's age add up to 140 and also that his age plus his father's age add up to 105 Furthermore,he says that the sum of his age and his mother's age is 30 more than his father's age.Calculate the man's age or show that his hints contradict one another.
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
twice his mother's age add up to 140 and also that his age plus his father's age add up to 105 Furthermore,he says that the sum of his age and his mother's age is 30 more than his father's age
:
Let x = man's age
Let m = mother's age
Let f = father's age
:
Write an equation for each statement
"twice his mother's age add up to 140"
2m = 140
m = 70
:
"also that his age plus his father's age add up to 105"
x + f = 105
:
"the sum of his age and his mother's age is 30 more than his father's age"
x + m = f + 30
Replace m with 70
x + 70 = f + 30
x - f = 30 - 70
x - f = -40
Add this equation to x + f = 105
x - f = -40
x + f = 105
-------------- adding eliminates f, find x
2x = 65
x =
x = 32.5 is the man's age, we hope for an integer here, but there it is!
:
:
Check solution in all statements
Find dad's age
32.5 + f = 105
f = 105 - 32.5
f = 72.5, father's age
:
"the sum of his age and his mother's age is 30 more than his father's age"
32.5 + 70 = 72.5 + 30
102.5 = 102.5, confirms our solution

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