The good ship Gemini is twice as old as its boiler was when the ship was as old as the boiler is now. If the sum of their ages is 49 years, how old is the ship? How old is the boiler?
Let s be the ship’s age, b the boiler’s age, and x be the unknown number of years ago.
Then s = 2(b – x) = 2b – 2x → 49 – b = 2b – 2x → 2x + 49 = 3b → x = (3b – 49)/2 (1)
But also, s – x = b → 49 – b – x = b → 49 – 2b = x. (2)
So: (3b – 49)/2 = 49 – 2b → 3b – 49 = 98 – 4b → 7b = 49 + 98 = 147 → b = 21.
Then s = 49 – 21 = 28. And s – x = b → 28 – x = 21 → x = 7.
Then s = 2(b – x) = 2b – 2x → 49 – b = 2b – 2x → 2x + 49 = 3b → x = (3b – 49)/2 (1)
But also, s – x = b → 49 – b – x = b → 49 – 2b = x. (2)
So: (3b – 49)/2 = 49 – 2b → 3b – 49 = 98 – 4b → 7b = 49 + 98 = 147 → b = 21.
Then s = 49 – 21 = 28. And s – x = b → 28 – x = 21 → x = 7.
Check: 28 = 2(21 – 7) = 2 · 14 and 28 – 7 = 21.