A farmer reared some ducks and chicks. A duck was sold at $15 and a
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?
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.
To solve this problem, we can break it down into steps.
Step 1: Determine the price of a chick.
We know that a duck was sold for $15. Therefore, the price of a chick would be 2/3 of $15.
Price of a chick = (2/3) * $15 = $10
Step 2: Calculate the total sales on the first day.
The farmer collected a total of $1140 from selling 1/3 of his poultry. We can use this information to find the total sales on the first day.
Total sales = $1140
Step 3: Determine the number of poultry sold and find out how many of them were chicks.
We know that 3/5 of the poultry sold were chicks. We can use this information to calculate the number of chicks sold.
Number of chicks sold = (3/5) * Total poultry sold
Step 4: Calculate the number of ducks sold on the first day.
The number of ducks sold can be determined by subtracting the number of chicks sold from the total poultry sold.
Number of ducks sold = Total poultry sold - Number of chicks sold
Step 5: Calculate the number of poultry the farmer had left after the first day.
The number of poultry the farmer had left after the first day can be calculated by subtracting the number of poultry sold on the first day from the total number of poultry.
Number of poultry left = Total poultry - Total poultry sold
Let's calculate the answers.
(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?