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?

Question

Mathematics

Cassie Bass

2 October, 01:37

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?

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Answers (1)

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Kristian Sampson · Answer 1

Answer: John had 72 pins originally.

Step-by-step explanation:

Let x represent the total number of pins that John had originally.

John divided his souvenir hat pins into two piles. The two piles had an equal number of pins. This means that each pile has x/2 pins.

He gave his brother one-half of one-third of one pile. This means that the number of pins that he gave his brother is

1/2 * 1/3 * x/2 = x/12 pins

The total amount left is

x/2 + (x/2 - x/12) = x/2 + 5x/12 = 11x/12

John had 66 pins left. Therefore

11x/12 = 66

11x = 66 * 12 = 792

x = 792/11 = 72