The ages of five sisters go up in steps of 3 years, each sister being 3 years older than the next one down. Their average age is 19 years. How old is the eldest sister?

Write the ages as a, a + 3, a + 6, a + 9 and a + 12. Evenly spaced ages are symmetric about the middle one, so the middle sister is the average: a + 6 = 19, giving a = 13. The ages are 13, 16, 19, 22 and 25, so the eldest is 25. (Check: they add to 95 and 95/5 = 19.) 22 adds one step of 3 to the average, which reaches the fourth sister, not the fifth. 13 is the youngest. 31 adds the whole spread of 12 years to the average, but the average sits in the middle of the spread, so only half of it lies above.