A farmer had 250 ducks and 150 chickens. He gave a total of 100 chickens to his sister. Later, the farmer bought 5 more ducks and 35 chickens. As a result, the number of ducks decreased by 10% and the number of chickens increased by 20%. A) How many ducks did the farmer give away? B) How many chickens did he give away?
I'm confused because I keep getting 30 ducks and 5 chickens but that doesn't equal 100.
I guess it was supposed to say
He gave a total of 100 ducks and chickens to his sister.
If he gave away d ducks and c chickens, then
250-d+5 = 9/10 * 250 ==> d = 30
150-c+35 = 6/5 * 150 ==> c = 5
Something's fowl here, I agree.
Let's break down the problem step by step:
Given:
- The farmer had 250 ducks and 150 chickens.
- He gave a total of 100 chickens to his sister.
- Later, he bought 5 more ducks and 35 chickens.
- As a result, the number of ducks decreased by 10%, and the number of chickens increased by 20%.
A) How many ducks did the farmer give away?
1. Initially, the farmer had 250 ducks.
2. He bought 5 more ducks, so the total number of ducks becomes 250 + 5 = 255.
3. The number of ducks decreased by 10%, which means there was a reduction of 10/100 * 255 = 25.5 ducks.
4. Subtracting the reduction from the total number of ducks gives 255 - 25.5 = 229.5 ducks.
5. Since we cannot have half a duck, the farmer gave away 229 ducks.
B) How many chickens did he give away?
1. Initially, the farmer had 150 chickens.
2. He gave a total of 100 chickens to his sister, so the number of chickens becomes 150 - 100 = 50.
3. He bought 35 more chickens, so the total number of chickens becomes 50 + 35 = 85.
4. The number of chickens increased by 20%, which means there was an addition of 20/100 * 85 = 17 chickens.
5. Adding the addition to the total number of chickens gives 85 + 17 = 102 chickens.
6. So, the farmer gave away 102 - 150 = -48 chickens, which doesn't make sense.
It seems there might be an error in the problem statement or calculations. Please double-check the information provided to find any discrepancies or missing details.
To solve this problem, let's break it down step by step:
Step 1: Calculate the starting number of ducks and chickens.
The farmer initially had 250 ducks and 150 chickens.
Step 2: Calculate the number of chickens the farmer gave away.
The farmer gave away 100 chickens to his sister. So the new number of chickens will be 150 - 100 = 50 chickens.
Step 3: Calculate the new number of ducks.
Since the number of ducks decreased by 10%, we can calculate the decrease as follows:
10% of 250 ducks = (10/100) * 250 = 25 ducks.
Therefore, the new number of ducks is 250 - 25 = 225 ducks.
Step 4: Calculate the new number of chickens.
Since the number of chickens increased by 20%, we can calculate the increase as follows:
20% of 50 chickens = (20/100) * 50 = 10 chickens.
Therefore, the new number of chickens is 50 + 10 = 60 chickens.
Step 5: Calculate the total number of ducks and chickens after the transactions.
The total number of ducks is 225 (from step 3) + 5 (5 more ducks bought later) = 230 ducks.
The total number of chickens is 60 (from step 4) + 35 (35 more chickens bought later) = 95 chickens.
Step 6: Calculate the number of ducks the farmer gave away.
The difference in the starting number of ducks (250) and the current number of ducks (230) gives us the number of ducks the farmer gave away: 250 - 230 = 20 ducks.
Step 7: Calculate the number of chickens the farmer gave away.
The difference in the starting number of chickens (150) and the current number of chickens (95) gives us the number of chickens the farmer gave away: 150 - 95 = 55 chickens.
Therefore, the farmer gave away 20 ducks and 55 chickens in total.
It seems that your initial calculation of 30 ducks and 5 chickens as the answer did not account for the decrease of 10% in the number of ducks and the increase of 20% in the number of chickens.