Question

McDonald has 69 water troughs for animals to drink from. Horses drank from horse troughs exactly 2 for each trough. Cows drank from cow troughs exactly 3 per trough and pigs drank from pig troughs, exactly8 per trough. McDonald has the same number of horses cows and pigs. How many animals does mcdonald have?

Answer 1

216 animals

Explanation:

Let n represent the number of each type of animal.

Since there are two horses for every horse trough, then n must be divisible by 2. Since there are three cows for every cow trough, then n must be divisible by 3. Since there are eight pigs for every pig trough, then n must be divisible by 8. Therefore, n must be divisible by 2, 3 and 8. The smallest number divisible by 2, 3, and 8 is 24. (This number is called the lowest common multiple or LCM, for short.)

If there are 24 of each kind of animal, there would be 24 ÷ 2 = 12 troughs for horses, 24 ÷ 3 = 8 troughs for cows and 24 ÷ 8 = 3 troughs for pigs. This would require a total of 12 + 8 + 3 = 23 troughs. Since there are 69 troughs and

69 ÷ 23 = 3, we require 3 times more of each type of animal. That is, there would be 24 × 3 = 72 of each type of animal. The total number of animals is 72+72+72 or 216.

Therefore, McDonald has 216 animals.

Hope this helps :)