The ratio of cats to dogs at a shelter is 3:5. If there are 24 cats, how many dogs are there?

Set up the ratio as a proportion. Cats/dogs = 3/5 = 24/x. Cross-multiply: 3x = 120. Solve: x = 40 dogs. Alternative: cats are 3 'parts', and there are 24 actual cats; so each 'part' = 24/3 = 8. Dogs are 5 parts; 5 × 8 = 40 dogs. Total animals would be 24 + 40 = 64, with 3:5 ratio confirmed (24:40 reduces to 3:5). Ratios appear in many ASVAB problems. Key skills: (1) Setting up the proportion correctly with matching units; (2) Solving by cross-multiplication; (3) Understanding part-to-part vs part-to-whole ratios. Part-to-part is the actual ratio (3:5); part-to-whole compares one part to the total (3/8 for cats, 5/8 for dogs). Be careful which form the problem asks for. Inverse ratios (when one variable goes up as another goes down) are different — for example, more workers means less time per worker.