2012 AMC 10A Problem 5

Below is the professionally curated solution for Problem 5 of the 2012 AMC 10A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2012 AMC 10A solutions, or check the answer key.

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Concepts:fraction mean

Difficulty rating: 870

Last year $100$ 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 $4.$ What was the total number of cats and kittens received by the shelter last year?

$150$

$200$

$250$

$300$

$400$

Solution:

We have that there are $100 \div 2 = 50$ female cats. We then have that $50 \div 2 = 25$ cats that have kittens.

Since the average number of kittens per litter is $4,$ the total number of kittens is $4 \cdot 25 = 100.$

The total number of cats and kittens is then $100 + 100 = 200.$

Thus, B is the correct answer.

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