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Piano Lessons		  
Q Abigail, Bettina, Cynthia, and Dahlia all began piano lessons last year. Cynthia took twice as many lessons as Bettina. Abigail took 4 lessons more than Dahlia but 3 fewer than Cynthia. Dahlia took 15 lessons altogether.

How many lessons did Bettina take?


  
A Bettina took 11 lessons.

Let A stand for Abigail, B for Bettina, and so on. C = 2B A = D + 4 = C - 3 D = 15

Since D = 15, you know that A = 19. You also know that C - 3 = 19, which means that C = 22. And since C = 2B, 22 = 2B, which means that B = 11.

Source: Inspired by a similar puzzle inUnriddlingby Alvin Schwartz, New York: Lippincott, 1983.