Daniel, my son, is exactly one fifth of my age. in 21 years time, i will be exactly twice his age. my wife is exactly seven times older than my daughter, jessica. in 8 years time, my wife will be three times older than jessica. how old are daniel and jessica now?
let daniel's age = d and let jessica's age = j let your current age = x and your wife's current age = y
x = 5d (given in question) ∴ x - 5d = 0
x + 21 = 2(d+21) (given in question) ∴ x + 21 = 2d + 42 ∴ x - 2d = 21
We can solve these two rearranged equations simultaneously by multiplying the first equation by -1 and adding them. This gives us the following:
3d = 21 ∴ d = 7
This means that daniel is currently 7 and (if we substitute d = 7 into one of the equations) you are 35. We use a similar method for your wife's and jessica's current ages.
y = 7j (given in question) ∴ y - 7j = 0
y + 8 = 3(j + 8) ∴y + 8 = 3j + 24 ∴ y - 3j = 16
If we use a similar method of elimination we get this:
4j = 16 ∴ j = 4
Hence, from this we can concur that daniel is 7 and jessica is 4.
