Math Problem Statement
A chef is estimating the cost to prepare a fixed-price menu for x guests. The anticipated cost of the appetizers is a(x) = 3.25x, the anticipated cost for the main course is m(x) = 5.25x, and the anticipated cost for the dessert course is d(x) = 1.25x. If the functions are combined so that c(x) = a(x) + m(x) + d(x), then the function c(x) includes the point (40,
Solution
To find the function that includes the point , we first need to combine the given functions , , and .
Given:
- (cost of appetizers)
- (cost of the main course)
- (cost of dessert)
The total cost function is the sum of these three functions:
Substituting the expressions for , , and :
Now, combine like terms:
So, the function is:
We are given that the function includes the point . To find , substitute into the function:
Thus, the point is .
Would you like more details or have any questions? Here are five related questions:
- What would the cost be for 50 guests?
- How would the cost function change if the price of the main course increased by $2 per guest?
- What is the total cost for 100 guests?
- How would you adjust the function if the dessert cost doubled?
- What is the individual contribution of each course to the total cost for 40 guests?
Tip: Always check your function by substituting values to ensure the calculations are consistent with given points.
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Math Problem Analysis
Mathematical Concepts
Functions
Linear Equations
Cost Analysis
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12
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