Verified Answer :

\(1:4=\frac{1}{4}\\\\d-number\ of\ dogs;\ c-number\ of\ cats\\\\d:c=1:4\to\frac{d}{c}=\frac{1}{4}\\\\d=7\ therefore\\\\\frac{7}{c}=\frac{1}{4}\ \ \ \ |cross\ multiply\\\\1\cdot c=7\cdot4\\\\\boxed{c=28}\leftarrow answer\)

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