Answer: To solve for the number of each type of pizza sold, let's use a step-by-step approach.
Step 1: Let's assume the number of plain pizzas sold is 'x' and the number of supreme pizzas sold is 'y'.
Step 2: We know that the cost of plain pizzas is $13 each, so the revenue generated from selling plain pizzas would be 13x dollars.
Step 3: Similarly, the cost of supreme pizzas is $17 each, so the revenue generated from selling supreme pizzas would be 17y dollars.
Step 4: The profit from plain pizzas is the revenue generated from selling plain pizzas minus the cost of the ingredients for plain pizzas. We are told that the profit from plain pizzas is the same as the profit from supreme pizzas.
Step 5: The cost of ingredients for plain pizzas is $310 per week, so the profit from selling plain pizzas would be 13x - 310 dollars.
Step 6: The cost of ingredients for supreme pizzas is $450 per week, so the profit from selling supreme pizzas would be 17y - 450 dollars.
Step 7: Since the profit from plain pizzas is equal to the profit from supreme pizzas, we can equate the two expressions from Step 5 and Step 6:
13x - 310 = 17y - 450
Step 8: Simplifying the equation, we get:
13x - 17y = -140
Step 9: We need to find the values of 'x' and 'y' that satisfy this equation.
There are multiple solutions to this equation. One possible solution is:
Let's assume 'x' to be 2 and 'y' to be 3. Substituting these values into the equation from Step 9, we get:
13(2) - 17(3) = -140
26 - 51 = -140
-25 = -140
The equation is not satisfied with this assumption of 'x' and 'y', which means this is not the correct solution.
To find the correct solution, we need additional information or constraints to narrow down the possibilities.