A farmer reared some ducks and chicks. A duck was sold at $15 and a

Question

chick was sold at 2/3 of that price. On the first day, the farmer sold 1/3 of his poultry and collected $1140 from the sale. 3/5 of the poultry sold were chicks.
(a) How many of the ducks were sold on the first day?
(b) How many of the poultry did the farmer have left after the first day?

Answer 1

Let x be the number of ducks and y be the number of chicks.
From the given information, we can create a system of equations:
x + y = total number of poultry
15x + (2/3)(15x) = 1140 (total revenue from sales)
Simplifying the second equation:
15x + 10x = 1140
25x = 1140
x = 45
So the farmer had 45 ducks. To find the number of chicks:
3/5(x+y) = number of chicks sold
3/5(45+y) = number of chicks sold
27 + 3/5y = number of chicks sold
And we know that the total number of poultry sold on the first day was 1/3(x+y):
1/3(45+y) = total number of poultry sold
15 + 1/3y = total number of poultry sold
Setting these two equations equal to each other:
27 + 3/5y = 15 + 1/3y
12 = 1/15y
y = 180
So the farmer had 180 chicks. Therefore, after the first day, the farmer had:
45 + 180 - (1/3)(45+180) = 135 poultry left.