95
92
Given 160 heads and 450 legs, we aim to determine the number of ducks (\(d\)) and rabbits (\(r\)) in the zoo. Each animal has one head, leading to the first equation:
\(d + r = 160\)
Ducks have 2 legs and rabbits have 4 legs, forming the second equation:
\(2d + 4r = 450\)
Simplifying the second equation by dividing by 2 yields:
\(d + 2r = 225\)
We now have the system of linear equations:
\(1. \quad d + r = 160\)
\(2. \quad d + 2r = 225\)
Subtracting equation 1 from equation 2:
\((d + 2r) - (d + r) = 225 - 160\)
\(r = 65\)
Substituting the value of \(r\) back into equation 1:
\(d + 65 = 160\)
\(d = 160 - 65\)
\(d = 95\)
Consequently, there are 95 ducks in the zoo.