d = s + 26 (Daniel is 26 years older than his son)
d + 6 = 3(s + 6) (in six years time, Dan'll be 3 times as old as his son)
We have a value for d, so let's plug it in:
s + 26 + 6 = 3(s + 6)
Simplify and distribute:
s + 32 = 3s + 18
Subtract s:
32 = 2s + 18
Subtract 18:
14 = 2s
Divide by 2:
7 = s
d = 7 + 26
d = 33
If Daniel is currently 26 years older than his son, and in six years he will be three times older than his son, then:
Daniel is 33 years old
Daniel's son is 7 years old
Let the current age of Daniel be y
Let the current age of Daniel's son be x
Daniel is currently 26 years older than his son
y = x + 26........(1)
In six years time:
Daniel's age will be y + 6
Daniel's son's age will be x + 6
In six years, Daniel will be three times older than his son
y + 6 = 3(x + 6)
y + 6 = 3x + 18
y = 3x + 18 - 6
y = 3x + 12......(2)
Let equations (1) and (2) be equal to each other
x + 26 = 3x + 12
3x - x = 26 - 12
2x = 14
x = 14/2
x = 7
Substitute x = 7 into equation (1)
y = x + 26
y = 7 + 26
y = 33
Daniel is 33 years old
Daniel's son is 7 years old
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