There are d black and brown horses in a field. There are 16 more black horses than brown horses. Of the horses in the field, only 25% of them are brown. How many are black?

Answer: 24 black horses

Step-by-step explanation:

Let the number of black horses = bl and

The number of Brown horses = br

Total number of horses = d

Of the horses in the field, only 25% of them are brown. That is,

25% of d = br

0.25d = br ... (1)

The remaining horses are black. Which will be 100% - 25% = 75%. That is,

75% of d = bl

0.75d = bl ... (2)

But according to the question, there are 16 more black horses than brown horses. That is,

bl = br + 16 ... (3)

The total number of horses d will be

d = br + bl ... (4)

Substitute bl in equation 3 into equation 4

d = br + br + 16

d = 2br + 16 ... (5)

Substitutes equation (1) into the equation (5)

d = 2 (0.25d) + 16

d = 0.5d + 16

Collect the like terms

d - 0.5d = 16

0.5d = 16

d = 16/0.5

d = 32

Substitute 32 for d in equation (2).

bl = 0.75 * 32

bl = 24 horses.

Therefore, 24 horses are black.