Question

Michael is three times as old as Margaret, and in 6 years he will be twice as old as her. How old was Michael when Margaret was born?

Answer 1

Michael was 12 years old when Margaret was born.

Explanation:

Let Michael be x and Margaret be y.

x=3y

x+6 (years) = 2(6+y) --> x+6=12+2y --> x=6+2y

Now that we have x, substitute x=3y:

6+2y=3y --> y=6

Now we have y, substitute again with x=3(6) --> x=18

So, Michael, x, is 18 years old. Margaret, y, is 6 years old. But, to find how old Michael was when Margaret was born, do 18 (Michael's age)-6 (Margaret's age) to get 12. So, Michael was 12 years old when Margaret was born. Hope that helped, sorry if I missed something... :D

Answer 2

12 years old

Explanation:

m = Michael

a = Margaret

m = 3a

m+6 = 2(a+6)

m+6 = 2a+12

Two equations, two unknowns, so we can use substitution.

3a+6 = 2a+12

a+6 = 12

a = 6

Plug it back in.

m = 3(6)

m = 18

When Michael was 18, Margaret was 6. So when she was born (basically when she was 0) Michael was 18-6 = 12.