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.
The answer is 2/7 or 0.28571428... You can find this the same way as your other problem by finding the common denominator and multiplying. (Also, if you go on Mathway, you can find solutions to almost any problem really quickly.)
Hope this helps!
~Jessica
If this is what you meant...
