Mama mboga bought 244 tomatoes @100 for every 6 tomatoes, she sold them @sh72 for every 3 and the rest @60 for every 2. If she made the 65% profit, calculate the number of tomatoes sold @72 for every?

Let's first calculate the total cost of buying 244 tomatoes at 100 for every 6 tomatoes:

Cost per 6 tomatoes = 100
Cost per tomato = 100/6 = 16.67

Total cost of buying 244 tomatoes = 244 * 16.67 = 4066.68

Now, let's calculate the total revenue from selling the tomatoes:

Let x be the number of tomatoes sold @72 for every 3 tomatoes.
Then, the number of tomatoes sold @60 for every 2 tomatoes = 244 - x

Revenue from selling tomatoes @72 for every 3 tomatoes = x * (72/3) = 24x
Revenue from selling tomatoes @60 for every 2 tomatoes = (244 - x) * (60/2) = 30(244 - x)

Total revenue = 24x + 30(244 - x)

Since she made a 65% profit, we can set up the equation:

Total revenue = Total cost + 65% of Total cost
24x + 30(244 - x) = 4066.68 + 1.65 * 4066.68
24x + 7320 - 30x = 4066.68 + 6711.702
-6x = -3254.318
x = 542.386

Therefore, she sold 542 tomatoes @72 for every 3 tomatoes.

Step 1: Calculate the cost price of the tomatoes

Cost of 6 tomatoes = 100
Cost of 1 tomato = 100/6 = 16.67

Cost of 244 tomatoes = 16.67 - 244 = 4076.68

Step 2: Calculate the selling price of the tomatoes

1. Tomatoes sold at 72 for every 3:
Let x be the number of tomatoes sold at 72 for every 3.
Selling price of x tomatoes = 72 - x/3

2. Tomatoes sold at 60 for every 2:
Let y be the number of tomatoes sold at 60 for every 2.
Selling price of y tomatoes = 60 - y/2

Step 3: Calculate the total selling price

Total selling price = (72 - x/3) + (60 - y/2)

Step 4: Calculate the profit

Profit = (Total selling price - Cost price) - 100%
Profit = ((72 - x/3) + (60 - y/2) - 4076.68) - 100%

Step 5: Solve for x using the profit equation

Given that the profit is 65%, we have:
0.65 = ((72 - x/3) + (60 - y/2) - 4076.68) - 100%

Solving for x, we get:

x = 108.5

Therefore, Mama mboga sold 108 tomatoes @72 for every 3.