A village lost 14 percent of its goats in a flood and 6 percent of the remainder died from diseases given that number of goats left is 8084 find the original number of goats in the village?

Answer 1

Let G represent (take the place of) the original number of goats in the village.

Write down all the facts you know.

We started with G.

Then 14% died.

Then 6% of what was left died.

Then 8084 were left finally.

"Lost" and "died" suggest these are "take aways" ('-' signs). :^)

The first loss:
0.14G

The remainder after the first loss:
G - 0.14G

The second loss:
0.06 * (G - 0.14G)

G - two losses:
G - 0.14G - 0.06 * (G - 0.14G) = 8084

G - 0.14G - (0.06)(0.86G) = 8084

Factor out the G (so you can divide both sides "cleanly" leaving G on just one side:
G * (1 - 0.14 - 0.0516) = 8084
G * (0.8084) = 8084

Divide both sides by (0.8084) [note: dividing both sides of an EQUATION by the SAME number preserves EQUALITY]:
G = 8084/0.8084 = 10,000

Check:
10000 - 0.14 * 10000 = 10000 - 1400 = 8600

8600 - 0.06 * 8600 = 8600 - 6 * 86 = 8600 - 516 = 8084!

What might throw you is the phrase "of the remainder."

I took that to mean "the remainder after 14% died" which would be the 86% of the original still living after the flood.

Answer 2

Let the original number of goats be x. After losing 14%, there would be 0.86x goats left. Then, after 6% more die, there would be 0.94*0.86x = 0.8084x goats left. Given that 0.8084x = 8084, we find x = 10000, so the original number of goats was 10000 in the village.