Question

The sum of the ages of Alex and Amanda is 64 years. 8 years ago, Alex's age was 3 times Amanda'sage. How old is Alex now?

Answer 1

20 years

Step-by-step 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.

`\begin{gathered} y-8=3\mleft(x-8\mright) \\ \implies y=3(x-8)+8 \\ y=3x-24+8 \\ y=3x-16 \end{gathered}`

We substitute y=3x-16 into x+y=64.

`\begin{gathered} x+3x-16=64 \\ 4x=64+16 \\ 4x=80 \\ x=(80)/(4) \\ x=20 \end{gathered}`

Alex is 20 years old now.