8 A paddock contains both ducks and sheep. There are a total of 42 heads and 96 feet in the paddock. How many ducks and how many sheep are in the paddock?

Let's break it down! Each duck has 1 head and 2 feet, while each sheep has 1 head and 4 feet. If we let the number of ducks be \( D \) and the number of sheep be \( S \), we can form these equations: 1. \( D + S = 42 \) (total heads) 2. \( 2D + 4S = 96 \) (total feet) From the first equation, we can express sheep in terms of ducks: \( S = 42 - D \). Now, substitute \( S \) in the second equation: \( 2D + 4(42 - D) = 96 \) \( 2D + 168 - 4D = 96 \) Combine terms: \( -2D + 168 = 96 \) Subtract 168 from both sides: \( -2D = -72 \) Divide by -2: \( D = 36 \). Now, substituting \( D \) back into the first equation: \( 36 + S = 42 \) So, \( S = 42 - 36 = 6 \). Thus, there are 36 ducks and 6 sheep in the paddock!