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?
We can do this without algebra:
originally he had 500 ducks
the final number was 12% less , or 88% of the original
= 440 ducks
but that includes the purchase of 10 ducks, so the give-away must have been 70 ducks
so he must have given away 30 chickens
so his final count for chickens
= 300 - 30 + 75 (the new purchase) = 345
change = increase of 45 chickens
is this 15% of 300 ? YES
He gave his sister 70 ducks and 30 chickens
I believe the question is saying the total number of chickens and ducks the farm gave his sister was 100
Then we can create our equation
x=number of chicken gave away
y=number of duck gave away
300+75-x=300+(300)(0.15)
375-x=345
x=30
Number of chick gave away is 30
After that, because we know the number of chicken and duck gave away in total is 100, so
x+y=100
replace x with 30
30+y=100
y=70
Number of duck gave away is 70
OR if you want to double check your answer, you create a equation for duck
500+10-y=500-(500)(0.12)
510-y=440
y=70
Farmer gave away 30 chickens and 70 ducks to his sister
a) Well, ducks sure know how to migrate! Let's break it down. The farmer initially had 500 ducks and the number decreased by 12%. So we take 12% of 500 which is 500 x 0.12 = 60. The farmer must have given away 60 ducks.
b) As for the chickens, the farmer started with 300 of them. Then, he gave away 100 chickens and ducks. So let's subtract 100 from the initial 300 to get 300 - 100 = 200 chickens. But hold your horses, the chickens have an exciting tale to tell too! They increased by 15%. We'll take 15% of 200 which is 200 x 0.15 = 30. After this hencredible transformation, the farmer had 200 + 30 = 230 chickens.
So, the farmer gave away 60 ducks and 100 chickens.
Let's break down the problem step by step:
Step 1: Calculate the number of chickens and ducks after giving away 100 animals to the farmer's sister:
- The farmer started with 500 ducks and 300 chickens.
- After giving away 100 animals, he has 500 - 100 = 400 ducks.
- He also has 300 - 100 = 200 chickens.
Step 2: Calculate the number of animals after buying 10 more ducks and 75 more chickens:
- The farmer now has 400 + 10 = 410 ducks.
- He also has 200 + 75 = 275 chickens.
Step 3: Determine the percent change in the number of ducks:
- The original number of ducks was 500, and now it is 410.
- The percent decrease in the number of ducks is (500 - 410) / 500 * 100% = 90 / 500 * 100% = 0.18 * 100% = 18%.
Step 4: Determine the percent change in the number of chickens:
- The original number of chickens was 300, and now it is 275.
- The percent increase in the number of chickens is (275 - 300) / 300 * 100% = -25 / 300 * 100% = -0.08333 * 100% = -8.33%.
Step 5: Calculate the absolute change in the number of ducks:
- The absolute change in the number of ducks is 18% * 500 ducks = 0.18 * 500 = 90 ducks.
Step 6: Calculate the absolute change in the number of chickens:
- The absolute change in the number of chickens is 8.33% * 300 chickens = 0.08333 * 300 = 24.99 chickens (approximately 25 chickens).
Step 7: Calculate the number of ducks the farmer gave away:
- The farmer initially had 500 ducks and now has 410 ducks.
- The number of ducks he gave away is 500 - 410 = 90 ducks.
Step 8: Calculate the number of chickens he gave away:
- The farmer initially had 300 chickens and now has 275 chickens.
- The number of chickens he gave away is 300 - 275 = 25 chickens.
Therefore, the farmer gave away 90 ducks and 25 chickens.
To solve this problem, we can follow these steps:
Step 1: Calculate the initial number of ducks and chickens.
The farmer initially had 500 ducks and 300 chickens.
Step 2: Calculate the number of ducks and chickens given away.
The farmer gave away a total of 100 ducks and chickens to his sister.
Step 3: Calculate the new number of ducks and chickens.
After giving away the ducks and chickens, we subtract the number given away from the initial amount. Therefore, the new number of ducks is 500 - 100 = 400, and the new number of chickens is 300 - 100 = 200.
Step 4: Calculate the number of ducks and chickens bought later.
The farmer bought 10 more ducks and 75 more chickens. We add these amounts to the new count after giving some away. Therefore, the new number of ducks is 400 + 10 = 410, and the new number of chickens is 200 + 75 = 275.
Step 5: Calculate the decrease in the number of ducks.
To find the decrease in the number of ducks, we need to find 12% of the initial number of ducks. We multiply 500 by 12% (or 0.12) to get 500 * 0.12 = 60 ducks.
Step 6: Calculate the increase in the number of chickens.
To find the increase in the number of chickens, we need to find 15% of the initial number of chickens. We multiply 300 by 15% (or 0.15) to get 300 * 0.15 = 45 chickens.
Step 7: Calculate the final number of ducks.
We subtract the decrease in the number of ducks from the new count. Therefore, the final number of ducks is 410 - 60 = 350.
Step 8: Calculate the final number of chickens.
We add the increase in the number of chickens to the new count. Therefore, the final number of chickens is 275 + 45 = 320.
Now, we can answer the questions:
a) How many ducks did the farmer give away?
The farmer gave away a total of 100 ducks.
b) How many chickens did he give away?
The farmer also gave away 100 chickens.