I.Q. Questions: Two-Legged and Four-Legged Counting
1. A group consists of some humans and cows, where the number of heads is 80 and the number of legs is 200. How many humans are in the group?
Answer: 60
Solution: Let \( H \) be the number of humans and \( C \) be the number of cows. Each has one head, so \( H + C = 80 \). Humans have 2 legs and cows have 4 legs, so \( 2H + 4C = 200 \). Simplifying the second equation: \( H + 2C = 100 \). Subtracting the first from the second: \( (H + 2C) - (H + C) = 100 - 80 \implies C = 20 \). Then, \( H + 20 = 80 \implies H = 60 \). Thus, the number of humans is 60.
2. A group consists of some humans and cows, where the number of heads is 65 and the number of legs is 210. How many cows are in the group?
Answer: 40
Solution: Let \( H \) be the number of humans and \( C \) be the number of cows. Then, \( H + C = 65 \) and \( 2H + 4C = 210 \). Simplifying the second equation: \( H + 2C = 105 \). Subtracting the first from the second: \( (H + 2C) - (H + C) = 105 - 65 \implies C = 40 \). Thus, the number of cows is 40.
3. A group consists of some cows and humans, where the number of legs is 12 more than twice the number of heads. How many cows are in the group?
Answer: 6
Solution: Let \( H \) be the number of humans, \( C \) be the number of cows, and \( T = H + C \) be the total number of heads. The number of legs is \( L = 2H + 4C \). Given \( L = 2T + 12 \), substitute \( T = H + C \): \( 2H + 4C = 2(H + C) + 12 \). Simplify: \( 2H + 4C = 2H + 2C + 12 \implies 2C = 12 \implies C = 6 \). Thus, the number of cows is 6.
Note: For a visual explanation of these solutions, watch the video titled "I.Q. Two-Legged and Four-Legged Counting". Subscribe to our channel for more such content!
