The two brothers
Number Theory
Level
pending
One brother says of his younger brother: “Two years ago, I was three times as old as my brother was. In three years’ time, I will be twice as old as my brother.” How old is the older brother? Good luck!=)
12
19
14
16
18
17
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1 solution
Older brother is x years old and younger brother is y years old (or young?).
x – 2 = 3(y – 2) = 3y – 6
x + 3 = 2(y + 3) = 2y + 6
x = 3y – 6 + 2 = 3y – 4
= 2y + 6 – 3 = 2y + 3
3y – 4 = 2y + 3
3y – 2y = 3 + 4
y = 7
x = 2y + 3
= 2 × 7 + 3
= 17