Final answer:
To solve the profit calculation problem, the fruiterer's total cost and desired revenue were computed, leading to an equation based on the number of pineapples sold at each price. Solving this equation determined the number of pineapples sold at sh.72 for every three to be 120 pineapples.
Step-by-step explanation:
The question is a profit calculation problem in mathematics, asking to determine the number of pineapples sold at a given price to achieve a certain profit margin. To solve this, we need to calculate the total cost, the desired total revenue to get a 65% profit, and then find the correct mix of pineapples sold at each price point that satisfies this condition.
First, we calculate the total cost of the pineapples:
- The fruiterer bought 144 pineapples at sh.100 for every 6 pineapples.
- Total cost = (144 pineapples / 6) × sh.100 = 24 × sh.100 = sh.2400.
To achieve a 65% profit, the total revenue should be:
- Total revenue = Total cost + (65% of Total cost).
- Total revenue = sh.2400 + (0.65 × sh.2400).
- Total revenue = sh.2400 + sh.1560 = sh.3960.
Now, let's denote the number of pineapples sold at sh.72 for every three as 'x' and the rest, which is (144 - x) pineapples, at sh.60 for every two. The total revenue can be given by the equation:
- (x / 3) × sh.72 + ((144 - x) / 2) × sh.60 = sh.3960.
Solving this equation, we find that 'x', the number of pineapples sold at sh.72 for every three, is 120 pineapples. Therefore, the correct answer is c) 120 pineapples.