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PSAT/NMSQT
PSAT Math Test - No Calculator Section

Minimizing Basic Model Production Under Budget Constraints

Very Hard Heart Of Algebra Linear Equations And Inequalities

A remote-control aircraft company produces two types of models: Basic and Advanced. The cost to produce each Basic model is given by the equation:

$$C_B = 50 + 15x$$

where $C_B$ is the total cost for producing $x$ Basic models. Similarly, for the Advanced models, the equation is:

$$C_A = 75 + 20y$$

where $C_A$ is the total cost for producing $y$ Advanced models. The company wants to minimize the production costs while maintaining a total budget of $C_T$ such that:

$$C_T ext{ (total budget)} = C_B + C_A$$

What is the minimum number of Basic models they can produce if they decide to produce 10 Advanced models, while still adhering to this budget? Write your answer as a whole number.

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