Question

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

Answer 1

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.

Answer 2

x=60