Adam, Brian, and Casey are all brothers. Brian is three years less than twice Casey's age. Adam is 9 years older than Casey. The sum of their ages is 46. How old is each of the brothers

Let Casey's age be x

Brian's age will be - 3 from 2 times x (Casey's age) so it will be 2x-3

Adam's age will be Casey's age (x) + 9 which is x+9

NOW the sum of all these ages is 46 so ...

Casey's age + Brian's age + Adam's age = 46

x + 2x-3 + x+9 = 46

2x + x + x + 9 - 3 = 46

4x + (9 - 3) = 46

4x - 6 = 46

now transfer the numbers on the left one by one to the other side (right)

4x = 46 - 6 (always remember the sign of the number becomes the opposite when we transfer them to other side)

4x = 40

x = 40 / 4

x = 10

so x = Casey's age = 10

2x - 3 = Brian's age = 2 * 10 - 3

= 20 - 3 = 17

x + 9 = Adam's age = 10 + 9 = 19