An individual ordered 5 pairs of black socks and an unknown number of brown sock pairs. Each black pair costs three times as much as a brown pair. However, when preparing the bill, the clerk mistakenly swapped the quantities of black and brown socks, resulting in the total bill doubling. How many pairs of brown socks were originally ordered?

Explanation

Let the number of brown sock pairs ordered be x, and let the price of one brown pair be Y. The total cost of the original order is 5 × 3Y (for black socks) plus x × Y (for brown socks), which is 15Y + xY. When the quantities are swapped, the cost becomes x × 3Y plus 5 × Y, or 3xY + 5Y. The problem states that the mistaken bill is twice the original, so: 3xY + 5Y = 2(15Y + xY) Simplifying: 3xY + 5Y = 30Y + 2xY 3xY - 2xY = 30Y - 5Y xY = 25Y x = 25 Therefore, the original order included 25 pairs of brown socks.