A fruitier bought 144 pineapples at $10 for every six pineapples. Sh sold some of them at $12 for every three and the rest at $6 for every two. If she made a 65% profit, calculate the number of pineapples sold at $12 for every three

If she sold x at $12/3, then the rest (144-x) were sold at $6/2. So,

x(12/3)+(144-x)(6/2) = (144)(10/6)(1.65)
x = -36

Negative pineapples? How is that possible?

Look:
she paid 10/6 = $1.67 per pineapple.
Some she sold at $4 each, and some at $3 each.

To make 65% profit, she'd have had to sell them all at an average price of 1.67*1.65 = $2.75

But, she made more than that on every pineapple! So, there's a typo somewhere in your exposition.

Hmmm. 65% profit based on selling price means 1/.35 = 2.857 based on cost. Let's try that.

x(12/3)+(144-x)(6/2) = (144)(10/6)(1/.35)
x = 253.7
No joy there, either.

x=60

To find out how many pineapples were sold at $12 for every three, we need to calculate the total number of pineapples sold and the number of pineapples sold at $6 for every two.

The fruitier bought 144 pineapples at $10 for every six pineapples.
So, the total cost of buying the pineapples is 144/6 * $10 = $240.

Since the fruitier made a 65% profit, the selling price must be $240 + ($240 * 65/100) = $240 + $156 = $396.

Let's assume the number of pineapples sold at $12 for every three is 'x.'

The selling price of 'x' pineapples at $12 for every three is x/3 * $12 = $4x.

The number of pineapples sold at $6 for every two is 144 - 'x.'

The selling price of (144 - x) pineapples at $6 for every two is (144 - x)/2 * $6 = $3 * (144 - x).

The total selling price is $4x + $3 * (144 - x) = $396.

Simplifying the equation $4x + $432 - $3x = $396 gives $1x = $396 - $432, which is - $36.

Since it's not possible to sell a negative number of pineapples, there must be an error in the problem information.

Please check the given information to resolve the discrepancy.

To solve this problem, we first need to determine the cost price of the pineapples.

The fruitier bought 144 pineapples at $10 for every six pineapples. We can determine the cost of each pineapple by dividing the total cost by the number of pineapples:

Cost per pineapple = Total cost / Number of pineapples
Cost per pineapple = $10 / 6 = $1.67 (rounded to two decimal places)

Next, we need to find out how much the fruitier sold the pineapples for.

Let's define:
x = the number of pineapples sold at $12 for every three
y = the remaining number of pineapples sold at $6 for every two

The total number of pineapples sold is the sum of x and y:
x + y = 144

We know that the fruitier made a 65% profit, so the total revenue is 65% more than the cost price of the pineapples.

The revenue from the pineapples sold at $12 for every three can be calculated as:
Revenue from x pineapples = x * ($12 / 3) = 4x

The revenue from the pineapples sold at $6 for every two can be calculated as:
Revenue from y pineapples = y * ($6 / 2) = 3y

The total revenue is the sum of the revenues from both types of pineapples:
Total revenue = Revenue from x pineapples + Revenue from y pineapples
Total revenue = 4x + 3y

We can set up an equation using the total revenue and cost price to solve for x:

Total revenue = Total cost + Profit
(4x + 3y) = (144 * $1.67) + (0.65 * Total cost)

Substituting the value of Total cost:
(4x + 3y) = (144 * $1.67) + (0.65 * (144 * $1.67))

Simplifying the equation:
4x + 3y = $240.48 + $155.28
4x + 3y = $395.76

We also know that x + y = 144, so we can substitute this value into the equation:
4x + 3(144 - x) = $395.76

Simplifying the equation further:
4x + 432 - 3x = $395.76
x + 432 = $395.76
x = $395.76 - 432
x = -$36.24

The value of x is negative, which doesn't make sense in this context. Therefore, there is an error in the problem statement or calculation.

Please double-check the information provided and try again.