A farmer had twice as many chickens as ducks on his farm. After he sold 166 chickens and ducks, he had half as many chickens as ducks left. How many chickens did the farmer have at first

The farmer have at first 202 chickens.

Step-by-step explanation:

Given:

A farmer had twice as many chickens as ducks on his farm. After he sold 166 chickens and ducks, he had half as many chickens as ducks left.

Now, to find the chickens farmer have at first.

Let the chickens be

And, the ducks be

As, the farmer had twice as many chickens as ducks on his farm.

So,    ......(1)

As, given the farmer after selling 166 chickens and ducks, he had half as many chickens as ducks left.

According to question:

Substituting the value of from equation (1) we get:

By cross multiplying we get:

Adding both sides 332 we get:

Subtracting both sides by we get:

Dividing both sides by 3 we get:

Now, to get the number of chickens substituting the value of in equation (1):

Therefore, the farmer have at first 202 chickens.

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