Two years ago a father was four times as old as his son. three years from now the father will be only three times as old as the son. how old is each now? if x represents the son's age two years ago, which expression represents his father's age three years from now? x + 3 3x + 3 3x + 15

Assume that the son's age two years ago was x and that the father's age two years ago was y
We are given that:
1- two years ago, the father's age was 4 times that of his son.
This means that: y = 4x > I
2- At present:
son's age = x + 2 and father's age is y + 2
3- three years from now:
son's age would be x+2+3 = x+5 and father's age would be y+2+3 = y+5
4- three years from now, the father's age would be three times as that of his son's.
This means that:
y + 5 = 3(x+5) > II

Substitute with equation I in II and solve for x as follows:
y+5 = 3x + 15
4x + 5 = 3x + 15
x = 10
x = 10 (age of son two years ago)

Now, substitute with x in equation I to get y as follows:
y = 4x = 4(10) = 40 (age of father two years ago)

This means that:
son's age now = 10 + 2 = 12 years old
father's age now = 40 + 2 = 42 years old

Hope this helps :)

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