Question

In a group of cows and hens, the number of legs is 14 more than twice the number of heads. The number of cows is:

• A. 5
• B. 7
• C. 10
• D. 12

Hint:

In animal head-leg problems, set up two equations: one for heads and one for legs, then solve simultaneously.

Answer 1

The Correct Option is B

Let the number of cows be $C$ and the number of hens be $H$.
Step 1: Each animal has one head, so the total number of heads is: \[ C + H \] Step 2: Each cow has 4 legs and each hen has 2 legs.
Total legs: \[ 4C + 2H \] Step 3: According to the problem, the number of legs is 14 more than twice the number of heads:
\[ 4C + 2H = 2(C + H) + 14 \] Step 4: Expand the right-hand side:
\[ 4C + 2H = 2C + 2H + 14 \] Step 5: Subtract $2H$ from both sides:
\[ 4C = 2C + 14 \] Step 6: Subtract $2C$ from both sides:
\[ 2C = 14 \] Step 7: Divide by 2:
\[ C = 7 \] Thus, the number of cows is $\mathbf7$.