Five years ago, a mother was twice as old as her son. in 6 years time, the sum of their age will be 82. find their present ages
Present age of son ---- x
present age of mother --- y
5 years ago:
son --- x-5
mother --- y-5
y-5 = 2(x-5)
y-5 = 2x - 10
2x - y = 5 or y = 2x - 5
6 years from now:
son --- x+6
mother ---- y + 6
x+6 + y+6 = 82
x + y = 70
x + 2x-5 = 70
3x = 75
x = 25 , then y = 2x-5 = 45
state your conclusion
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Good
Well, let's play with some numbers and have a laugh!
So, let's say the son is X years old right now. And since the mother was twice his age five years ago, we can just subtract 5 from his age, making the mother 2 times (X - 5) years old.
Now, if we fast forward six years, the son will be (X + 6) years old, and the mother will be 2 times (X - 5) + 6 years old.
According to the given information, the sum of their ages in 6 years will be 82. So, we can set up an equation:
(X + 6) + (2(X - 5) + 6) = 82
Simplifying this equation...
X + 6 + 2X - 10 + 6 = 82
3X + 2 = 82
3X = 80
X = 80/3
Well, it looks like we got a fractional answer! Now, I'm not sure how old either the son or the mother would be if one of them were a fraction of a year old. So, I'm going to bend the rules a bit and say that mathematically, it's not possible to determine their exact ages using the given information. But on the bright side, they're probably old enough to tell some funny jokes!
To solve this problem, we can set up a system of equations based on the given information.
Let's represent the mother's present age as M and the son's present age as S.
From the first statement, "Five years ago, a mother was twice as old as her son," we can create the equation:
M - 5 = 2(S - 5) --- (Equation 1)
From the second statement, "In 6 years' time, the sum of their age will be 82," we can create another equation:
(M + 6) + (S + 6) = 82 --- (Equation 2)
Now, let's solve this system of equations to find the values of M and S.
First, simplify Equation 1:
M - 5 = 2S - 10
M = 2S - 5
Now, substitute this expression for M in Equation 2:
(2S - 5 + 6) + (S + 6) = 82
2S + S + 7 = 82
3S = 82 - 7
3S = 75
S = 75 / 3
S = 25
Substitute the value of S back into Equation 1 to find M:
M = 2(25) - 5
M = 50 - 5
M = 45
Therefore, the mother's present age is 45 and the son's present age is 25.