Present ages:
Butch: x
Mr. Lucena: 2x
Ages 7 years ago (less 7):
Butch: x - 7
Mr. Lucena: 2x - 7
Equation:
Seven years ago, Mr. Lucena was 3 times as old as Butch:
2x - 7 = 3(x - 7)
2x - 7 = 3x - 21
-7 + 21 = 3x - 2x
14 = x
Substitute 4 to x:
Present ages:
Butch: x = 14 years old
Mr. Lucena: 2x = 2(14) = 28 years old
ANSWER: At present, Butch is 14 years old and Mr. Lucena is 28 years old.
Check:
Present ages: Mr Lucena is twice as old as Butch;
28 = 2(14)
28 = 28
Ages 7 years ago:
Butch: x - 7 = 14 - 7 = 7 years old
Mr. Lucena: 2x - 7 ⇒ 2(14) - 7 ⇒ 28 - 7 = 21 years old
Mr. Lucena is 3 times as old as Butch:
21 = 3(7)
21 = 21