Question

The sum of the ages of nick and Diana is 119 years. 12 years ago nicks age was 4 times Diana’s age. How old is nick now?

Answer 1

let

Nick age = x

Diana age= y

x + y = 119

12 years ago their age can be represented below

`\begin{gathered} 4(y-12)=x-12 \\ 4y-48=x-12 \\ x-4y=-36 \end{gathered}`
`\begin{gathered} x+y=119\ldots\ldots\ldots\ldots...(1) \\ x-4y=-36\ldots\ldots\ldots\ldots......\mathrm{}(2) \\ x=119-y \\ 119-y-4y=-36 \\ -5y=-36-119 \\ -5y=-155 \\ y=(-155)/(-5) \\ y=31 \\ x+31=119 \\ x=119-31 \\ x=88 \end{gathered}`

Nick's age= 88