### Instruction: John divided his souvenir hat pins into two piles. The two piles had an equal number of pins. He gave his brother one-half of one-third of one pile. John had 66 pins left. How many pins did John originally have?### Response: I need to find the original number of pins that John had, let's call it x.
I know that he divided them into two equal piles, so each pile had x/2 pins.
Then he gave his brother one-half of one-third of one pile, which is (1/2)(1/3)(x/2) = x/12 pins.
After that, he had 66 pins left, so I can write an equation: x - x/12 = 66.
To solve for x, I need to clear the fractions by multiplying both sides by 12: 12x - x = 792.
Simplifying, I get 11x = 792, so x = 792/11 = 72.
Therefore, John originally had 72 pins.