Gwen Is Twice As Old As Arni Was When Gwen Was As Old As Arni…
Gwen is twice as old as Arni was when Gwen was as old as Arni is now. If Gwen is 24 years old now, how old is Arni now?
[tex] \Large \mathbb{SOLUTION:} [/tex]
[tex] \begin{array}{l} \text{It is given that Gwen is }24\text{ years old now.} \\ \\ \text{Let }A\text{ be the present age of Arni and }x\text{ be the} \\ \text{number of years before present when Gwen} \\ \text{was as old as Arni is now.} \\ \\ \text{So we have the system of equations:} \\ \\ \begin{cases} 24 = 2(A – x)\!\!\!&\implies 12 = A – x \quad &(1) \\ 24 – x = A &\implies 24 = A + x &(2)\end{cases} \\ \\ \text{Adding }(1)\text{ and }(2),\text{ we get} \\ \\ \quad \quad \quad \quad \quad 36 = 2A \\ \quad \quad \:\: \implies \boxed{A = 18} \\ \\ \text{Thus, Arni is }18\text{ years old now.}\end{array} [/tex]
