five years ago, a mother was twice as old as her son. In 6 years time, the sum of their ages will be 82. Fiind their present age.
To solve this problem, let's assign variables to represent the mother's and son's present ages.
Let's say the mother's present age is represented by M.
And let's say the son's present age is represented by S.
From the problem, we have two pieces of information:
1) "Five years ago, a mother was twice as old as her son."
This can be written as:
M - 5 = 2(S - 5)
2) "In 6 years time, the sum of their ages will be 82."
This can be written as:
(M + 6) + (S + 6) = 82
Now we have a system of two equations:
M - 5 = 2(S - 5) (Equation 1)
(M + 6) + (S + 6) = 82 (Equation 2)
To solve this system, we can use the substitution method:
Step 1: Solve Equation 1 for M
M - 5 = 2S - 10
M = 2S - 5
Step 2: Substitute the value of M from Equation 1 into Equation 2
(2S - 5 + 6) + (S + 6) = 82
2S + 1 + S + 6 = 82
3S + 7 = 82
3S = 82 - 7
3S = 75
S = 75 / 3
S = 25
Step 3: Substitute the value of S back into Equation 1 to find M
M = 2S - 5
M = 2 * 25 - 5
M = 50 - 5
M = 45
Therefore, the present age of the mother is 45, and the present age of the son is 25.
Let x be mother and y be son
Equation 1 : x - 5 = 2*(y - 5)
Equation 2: x + 6 + y + 6 = 82
x - 5 = 2y -10 (1)
x + y + 12 = 82 (2)
x -2y = -5
x + y = 70 [Eliminate x]
-3y = -75
y = 25 [Son's age]
Sub y = 25 into x + y = 70
x + 25 = 70
x = 45 [Mother's age]
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