The Age of Bob and Carol is the same as Alice, in 2 years Alice will be twice as old as Bob and twice as old as Carol is today. How old are Bob,Carol and Alice today?

Question

Hello,

I did the task and want to ask if my answer is correct.

Bob= X, Carol=Y, Alice=Z

I Z= X+Y

II Z+2=2(X+2) <-> Z+2=2X+4

II Z+2=2Y

Now Sorting the equations

--> I Z-X-Y=0

II Z-2X = 2

II Z-2Y = -2

--> I Z-X-Y=0

II -Z+2X=-2

III -Z+2Y=2

--> I Z-X-Y=0

II X-Y=-2

III -X+Y=-2

At the end the second equation is equal to the third, therefore there exist an infinite amout of correct answers

Would be happy if someone can confirm :)

Answer 1

a = b+c, c=a-b

in 2 years

a+2 =2b = 2c

a+2 =2(b+2) = 2b +4

a = 2b +2

a = 2c +2

2b+2 = 2c+2

2b =2c

b = c, a =2b = 2c

if Alice is already double their age now

in 2 years she will no longer be double their age

so

No solution possible. DNE Does Not Exist