Question
Mrs. Rose bought a total of 60 chickens and turkeys and paid a sum of $292.80 for it. 2 days later, she sold 12 chickens and had and equal number of chickens and turkeys left. If each turkey cost $2.20 more than a chicken, how much did she pay for each turkey?
Answers
GPT 3.5
Let the number of chickens that Mrs. Rose bought be x.
Therefore, the number of turkeys she bought is 60 - x.
The total cost for the chickens is x * C, where C is the cost for each chicken.
Similarly, the total cost for the turkeys is (60 - x) * (C + $2.20), since each turkey cost $2.20 more than a chicken.
The total cost for all the chickens and turkeys is $292.80.
Therefore, x * C + (60 - x) * (C + $2.20) = $292.80.
Expanding the equation, we get xC + 60C - xC + 2.20 * (60 - x) = $292.80.
Simplifying the equation, we get 60C + 2.20 * 60 - 2.20x = $292.80.
Combining like terms, we get 60C + 132 - 2.20x = $292.80.
Subtracting $132 from both sides of the equation, we get 60C - 2.20x = $292.80 - $132.
Simplifying, we get 60C - 2.20x = $160.80.
Dividing both sides of the equation by 2.20, we get 27.27C - x = $72.72.
Adding x to both sides of the equation, we get 27.27C = x + $72.72.
The problem states that Mrs. Rose sold 12 chickens 2 days later and had an equal number of chickens and turkeys left.
Since the number of chickens left is equal to the number of turkeys left,
then x - 12 = 60 - x - 12.
Simplifying the equation, we get x - x = 60 - 12 - 12, which is 0 = 36.
This equation is not true, which means that our original assumption that the number of chickens and turkeys left is equal is incorrect.
Therefore, there must be a typo or error in the problem, since it is impossible to find the number of turkeys bought and the cost of each turkey without more information.
Therefore, the number of turkeys she bought is 60 - x.
The total cost for the chickens is x * C, where C is the cost for each chicken.
Similarly, the total cost for the turkeys is (60 - x) * (C + $2.20), since each turkey cost $2.20 more than a chicken.
The total cost for all the chickens and turkeys is $292.80.
Therefore, x * C + (60 - x) * (C + $2.20) = $292.80.
Expanding the equation, we get xC + 60C - xC + 2.20 * (60 - x) = $292.80.
Simplifying the equation, we get 60C + 2.20 * 60 - 2.20x = $292.80.
Combining like terms, we get 60C + 132 - 2.20x = $292.80.
Subtracting $132 from both sides of the equation, we get 60C - 2.20x = $292.80 - $132.
Simplifying, we get 60C - 2.20x = $160.80.
Dividing both sides of the equation by 2.20, we get 27.27C - x = $72.72.
Adding x to both sides of the equation, we get 27.27C = x + $72.72.
The problem states that Mrs. Rose sold 12 chickens 2 days later and had an equal number of chickens and turkeys left.
Since the number of chickens left is equal to the number of turkeys left,
then x - 12 = 60 - x - 12.
Simplifying the equation, we get x - x = 60 - 12 - 12, which is 0 = 36.
This equation is not true, which means that our original assumption that the number of chickens and turkeys left is equal is incorrect.
Therefore, there must be a typo or error in the problem, since it is impossible to find the number of turkeys bought and the cost of each turkey without more information.