Question

There are some horses on a farm of which 64% are young

horses and the remaining are little and old horses. The ratio of
little horses to old horses is 2:1. If there are 32 more young
horses than little horses, how many horses are on the farm?
horses
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Answer 1

There are a total of 122 horses on the farm.

Step-by-step explanation:

The question involves determining the number of horses on a farm based on given percentages and ratios. To solve this, we can set up a system of equations based on the available information. Let y be the number of young horses, l for little horses, and o for old horses. According to the problem, 64% of the horses are young, and young horses outnumber little horses by 32. The ratio of little to old horses is 2:1.

The system of equations can be set up as follows:

1. y = 0.64(y + l + o)
2. y = l + 32
3. l/o = 2/1

Using the second equation, y - l = 32, or y = l + 32. We then substitute y in the first equation and solve for l and o:

0.64(y + l + o) = y

0.64(l + 32 + l + o) = l + 32

0.64(2l + o + 32) - l = 32

1.28l + 0.64o + 20.48 - l = 32

l = 0.36l + 0.64o + 11.52

0.64l = 0.64o + 11.52

l = o + 18

Now that we know l = o + 18 and since l/o = 2/1, we can set o = x and then l = 2x. From l = o + 18, we get 2x = x + 18, which means x = 18 and l = 36.

Now we know the number of young horses y from y = l + 32 = 36 + 32 = 68. The total number of horses (y + l + o) is then 68 + 36 + 18 = 122.