Casey was twice as old as his sister 3 years ago. Now he is 5 years older than his sister. How old is Casey?

Let x is Casey's sister age.

3 years ago:

Casey was twice as old as his sister: 2a - 3

Now:

he is 5 years older than his sister: a + 5

2a - 3 = a + 5

subtract a to both sides

2a - 3 - a = a + 5 - a

simplify

a - 3 = 5

add 3 to both sides

a - 3 + 3 = 5 + 3

simplify

a = 8

His sister age is 8 years old now.

Now:

he is 5 years older than his sister: a + 5 = 8 + 5 = 13

proof:

so 3 years ago,

his sister age: 8 - 3 = 5

Casey age 3 years ago:

13 - 3 = 10 (C asey was twice as old as his sister 3 years ago)

Answer:

Casey is 13 years old now.