A farmer had 500 ducks and 300 chickens. He gave his sister 100 chickens and ducks. Later, the farmer bought 10 more ducks and 75 more chickens. As a result, the number of ducks decreased by 12% and the number of chickens increased by 15%.

a) How many ducks did the farmer give away?
b) How many chickens did he give away?

I got 70 ducks and 30 chickens for some reason.

Why do you say "for some reason"? Didn't you solve the problem?

Did you check your answer?
500-70+10 = 440 = 500 * 0.85 ok
300-30+75 = 375 = 345 * 1.15 ok

Here's how I did it. I imagine you did it in much the same way.

to start,
500 ducks
300 chickens

then gave away d ducks and c chickens,

At that point, he had
500-d ducks
300-c chickens

After buying more birds, he had
500-d+10 = 510-d ducks
300-c+75 = 375-c chickens

510-d = 500*.88 = 440
375-c = 300*1.15 = 345

d = 510-440 = 70
c = 375-345 = 30

Specifying that d+c = 100 was redundant.

a farmer had 15 animals in his farmyard somewhere chicken and some were cows.there were 52 legs in all . how many cows were in the farmyard?

😂 Thanks! 👍🏻

To solve this problem, let's break it down step by step:

Step 1: Calculate the original number of ducks before any changes were made.
The farmer originally had 500 ducks.

Step 2: Calculate the original number of chickens before any changes were made.
The farmer originally had 300 chickens.

Step 3: Calculate the total number of chickens and ducks before any changes were made.
The total number of animals before any changes were made is the sum of the ducks and chickens:
Total animals = 500 ducks + 300 chickens = 800 animals.

Step 4: Calculate the number of animals the farmer gave away to his sister.
The farmer gave his sister 100 chickens and ducks, so we subtract that from the total:
Total animals after giving away = 800 animals - 100 animals = 700 animals.

Step 5: Calculate the number of ducks the farmer had after giving some away.
We know that the number of ducks decreased by 12%. To find the new number of ducks, we multiply the original number of ducks by (100% - 12%):
New number of ducks = 500 ducks x (1 - 0.12) = 500 ducks x 0.88 = 440 ducks.

Step 6: Calculate the number of chickens the farmer had after giving some away.
We know that the number of chickens increased by 15%. To find the new number of chickens, we multiply the original number of chickens by (100% + 15%):
New number of chickens = 300 chickens x (1 + 0.15) = 300 chickens x 1.15 = 345 chickens.

Step 7: Calculate the total number of animals the farmer had after giving some away and making the changes.
Total animals after changes = New number of ducks + New number of chickens = 440 ducks + 345 chickens = 785 animals.

Step 8: Calculate the number of ducks the farmer bought.
The farmer bought 10 more ducks, so we add that to the new number of ducks:
New number of ducks after buying = 440 ducks + 10 ducks = 450 ducks.

Step 9: Calculate the number of chickens the farmer bought.
The farmer bought 75 more chickens, so we add that to the new number of chickens:
New number of chickens after buying = 345 chickens + 75 chickens = 420 chickens.

Therefore, the correct answers are:
a) The farmer gave away 500 ducks - 450 ducks = 50 ducks.
b) The farmer gave away 300 chickens - 420 chickens = 120 chickens.

So, the farmer gave away 50 ducks and 120 chickens, not 70 ducks and 30 chickens.