Krishan has some hens and some cows. If the total number of animal heads is 59 and the total number of feet is 190, how many cows does Krishan have?

## Concept & Strategy This is a standard system of linear equations word problem. We need to define variables for the two distinct items (hens and cows) and create two separate equations based on the given totals for heads and feet. ## Step-by-Step Solution * **Set up variables based on known attributes:** Let $H$ be the number of hens. (1 head, 2 feet) Let $C$ be the number of cows. (1 head, 4 feet) * **Create Equation 1 (Heads):** The total number of animal heads is 59. $H + C = 59$ * **Create Equation 2 (Feet):** The total number of feet is 190. $2H + 4C = 190$ * **Simplify Equation 2:** Divide the entire feet equation by 2 to make it easier to work with: $H + 2C = 95$ * **Solve the system of equations:** We now have: Eq 1: $H + C = 59$ Eq 2: $H + 2C = 95$ Subtract Eq 1 from Eq 2 to eliminate $H$: $(H + 2C) - (H + C) = 95 - 59$ $C = 36$ * Krishan has 36 cows. (If asked, hens would be $59 - 36 = 23$). ## Exam Strategy & Shortcut **The "Assume All" Shortcut:** Assume all 59 animals are the one with *fewer* legs (Hens). If all were hens, total feet = $59 \times 2 = 118$ feet. Given total feet = $190$. Difference = $190 - 118 = 72$ extra feet. These extra feet must belong to the cows, which have 2 *extra* feet each compared to a hen. Number of cows = $72 / 2 = 36$. This method avoids algebra entirely and can be done quickly on paper. ## Common Pitfall A common error is confusing which variable represents the 4-legged animal when setting up the feet equation, inadvertently writing $4H + 2C = 190$, leading to completely inverted answers. Always double-check your biological facts before writing the coefficients. ## Final Answer **Therefore, the correct answer is 36.**