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2012 AMC 10A Problem 5

Problem 5 of 25EasierAlgebra

Last year 100100 adult cats, half of whom were female, were brought into the Smallville Animal Shelter. Half of the adult female cats were accompanied by a litter of kittens. The average number of kittens per litter was 4.4. What was the total number of cats and kittens received by the shelter last year?

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Solution

We have that there are 100÷2=50100 \div 2 = 50 female cats. We then have that 50÷2=2550 \div 2 = 25 cats that have kittens. Since the average number of kittens per litter is 4,4, the total number of kittens is 4⋅25=100. 4 \cdot 25 = 100. The total number of cats and kittens is then 100+100=200. 100 + 100 = 200. Thus, B is the correct answer.

More practice

Concepts: fraction · mean

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.