Present ages:
Robin: x
Bruno: y
x + y = 45
y = 45 - x (Bruno's age)
Ages Seven years ago:
Robin: x - 7
Bruno: 45 - x - 7 or 38 - x
Equation:
x - 7 = ¹/₂ (38 - x) + 16
x - 7 = 19 - x/2 + 16
x + x/2 = 19 + 16 + 7
LCD: 2
(2)x + (2) x/2 = 42 (2)
2x + x = 84
3x = 84
3x/3 = 84/3
x = 28
Present ages:
Robin: x = 28 years old
Bruno: 45-x = 45 - 28 = 17 years old
ANSWER: Bruno is 17 years old
Ages Seven years ago:
Robin: 28 - 7 = 21 years old
Bruno: 17 - 7 = 10 years old
Seven years ago, Robin's age was 16 years more than 1/2 of Bruno's.
21 = 1/2 (10) + 16
21 = 5 + 16
21 = 21