Chicken Farmer's Puzzle: Solving for Chickens A chicken farmer has a total of 84 animals—some chickens and some cows—with 218 legs altogether. Chickens have 2 legs each, while cows have 4 legs each. Let's break this down step by step to find exactly how many chickens there are.

Setup Equations

Define variables: let ccc be the number of chickens and www be the number of cows.

  • Total animals: c+w=84c+w=84c+w=84.
  • Total legs: 2c+4w=2182c+4w=2182c+4w=218.

This is a classic system of linear equations, often seen in math problems like those on YouTube tutorials and homework sites.

Algebraic Solution

Simplify the legs equation by dividing by 2: c+2w=109c+2w=109c+2w=109. Subtract the animals equation from this:
(c+2w)−(c+w)=109−84(c+2w)-(c+w)=109-84(c+2w)−(c+w)=109−84
w=25w=25w=25. Then, c=84−25=59c=84-25=59c=84−25=59 chickens.

Verify: 59 chickens give 59×2=11859\times 2=11859×2=118 legs; 25 cows give 25×4=10025\times 4=10025×4=100 legs; total 218 legs.

Visual Guess-and-Check Method

Imagine all 84 animals as chickens: 84×2=16884\times 2=16884×2=168 legs (short by 50 legs).
Each cow "adds" 2 extra legs over a chicken, so 25 cows add 25×2=5025\times 2=5025×2=50 legs, confirming 59 chickens.

Method| Chickens| Cows| Total Animals| Total Legs
---|---|---|---|---
Algebraic| 59| 25| 84| 218 4
Guess-and-Check| 59| 25| 84| 218 1

Alternative Approaches

  1. Solve for chickens directly: From c=84−wc=84-wc=84−w, substitute into legs: 2(84−w)+4w=2182(84-w)+4w=2182(84−w)+4w=218, yielding w=25w=25w=25, c=59c=59c=59.
  1. Excess legs over minimum: 84 × 2 = 168; excess 50 legs means 25 cows (50 / 2).
  1. Graphing: Plot lines c+w=84c+w=84c+w=84 and 2c+4w=2182c+4w=2182c+4w=218; intersection at (59, 25).

This puzzle mirrors viral math riddles on forums like Reddit, with similar totals (e.g., 81 animals/220 legs = 52 chickens).

TL;DR: The farmer has 59 chickens.

Information gathered from public forums or data available on the internet and portrayed here.