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 (Casey was twice as old as his sister 3 years ago) Answer: Casey is 13 years old now.
