To solve this problem, we need to determine the value of x, which represents the number of lasagnas made by the cafeteria.
Let's break down the information given:
Number of lasagnas made: x
Number of cottage pies made: 100
Pounds of ground mince used for each lasagna: 2
Pounds of ground mince used for each cottage pie: 3
Total pounds of ground mince used: 500
We can set up the equation as follows:
Number of lasagnas made * Pounds of ground mince used for each lasagna + Number of cottage pies made * Pounds of ground mince used for each cottage pie = Total pounds of ground mince used
x * 2 + 100 * 3 = 500
Let's simplify and solve for x:
2x + 300 = 500
To isolate x, we subtract 300 from both sides of the equation:
2x + 300 - 300 = 500 - 300
2x = 200
To solve for x, we divide both sides of the equation by 2:
x = 200 / 2
x = 100
The value of x is 100.
#### 100
The answer is: 100
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
A school cafeteria uses ground mince to cook lasagnas and cottage pies. They make x lasagnas, which use 2 pounds of ground mince each, and cottage pies, which use 3 pounds of ground mince each. If the cafeteria has used 500 pounds of ground mince in total, They made 100 cottage pies. What is the value of unknown variable x?

### Answer:
