Answer:
20 years
Explanation:
Let Amanda's age = x
Let Alex's age = y
The sum of their ages is 64 years, therefore:
• x+y=64
Eight years ago, their ages were:
Amanda: (x-8)
Alex : (y-8)
Alex's age was 3 times Amanda's age.
• y-8 = 3(x-8)
We then solve the two resulting equations for x, Alex's age.
[tex]\begin{gathered} y-8=3\mleft(x-8\mright) \\ \implies y=3(x-8)+8 \\ y=3x-24+8 \\ y=3x-16 \end{gathered}[/tex]We substitute y=3x-16 into x+y=64.
[tex]\begin{gathered} x+3x-16=64 \\ 4x=64+16 \\ 4x=80 \\ x=\frac{80}{4} \\ x=20 \end{gathered}[/tex]Alex is 20 years old now.
