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?
a) How many ducks did the farmer give away?
b) How many chickens did he give away?
Answers
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
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
Explain ur answers more
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
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
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