Final answer:
Equations must be formed based on the information provided about the two types of candy mixes. These equations are graphed, and the intersection of the lines represents the solution meeting the chocolate requirements within the budget.
Step-by-step explanation:
To solve the question, we need to create a system of equations based on the given quantities of milk chocolate and white chocolate in the candy mixes, as well as the cost constraints and the required amounts of chocolates.
Let's denote x as the number of bags with nuts and y as the number of bags without nuts. Here are the two equations that represent the given information:
- 5x + y = 120 (milk chocolate requirement)
- 3x + 2y = 450 (white chocolate requirement)
We can also write an equation representing the total cost constraint:
50x + 6y = 3000
Graphing these equations on a coordinate plane will give us two lines, and the intersection point of these lines will be the solution, representing the number of each type of bags the store should purchase. We must also consider the non-negative constraints, meaning x and y cannot be negative since they represent quantities of candy bags.
To graph the equations, you need to determine the coordinates where each line intersects the axes, plot these points, and draw a line through them. The solution area is where all inequalities related to these equations overlap and will be shaded on the graph. This solution area represents the number of each type of bags (mix with nuts and mix without nuts) that the candy store can purchase to fulfill both the chocolate requirements and stay within the $3000 budget.