Billing error with sock pairs: A customer ordered 4 pairs of black socks and some pairs of brown socks. A black pair costs twice a brown pair. The clerk mistakenly swapped the counts of black and brown pairs on the bill, increasing the bill by 50%. What was the original ratio of black : brown pairs?

Introduction / Context:This question blends unit pricing with a mistaken interchange of quantities. It uses proportional reasoning to compare the correct bill with the incorrect one. Translating prices and quantities into algebra makes the comparison precise.

Given Data / Assumptions:

• Original order: 4 black pairs, x brown pairs.
• Black pair price = 2p; Brown pair price = p.
• Clerk swapped counts: billed 4 brown and x black.
• Mistake increased the bill by 50%.

Concept / Approach:Compute the correct bill B and mistaken bill B′, then use B′ = 1.5B to solve for x. Finally reduce the ratio 4 : x to simplest form.

Step-by-Step Solution:

Verification / Alternative check:Plug back x = 16: B = 8p + 16p = 24p; B′ = 4p + 32p = 36p = 1.5 * 24p. Works exactly.

Why Other Options Are Wrong:

• 2:1, 1:2, 4:1, 3:2: Do not satisfy B′ = 1.5B when substituted.

Common Pitfalls:Using “twice” as 2p more instead of 2p total, or interchanging prices rather than quantities.

Final Answer:1:4