Question

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?

Answer 1

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

Answer 2

Explain ur answers more

Answer 3

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