few_shots: Example:
Problem/activity:
You’re mixing ingredients for cookies. The recipe says to combine 6 tablespoons, or ¾ stick, of butter with 1 cup of sugar. You accidentally mix in a whole stick of butter (8 tablespoons) with the cup of sugar. How can you fix this?


Mathematical concept/skill options: 
A. Analyze proportional relationships and use them to solve real-world and mathematical problems.
B. Understand ratio concepts and use ratio reasoning to solve problems.


Your response:
Thought: This problem focuses on the ratio between two ingredients. Students do not have to analyze proportional relationships in-depth, which is reserved for a higher grade level, but rather use ratios to find missing values.
Answer: B

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_000972

6
options: Interpret functions that arise in applications in terms of the context.

Prove and apply trigonometric identities.

Interpret expressions for functions in terms of the situation they model.

Analyze functions using different representations.

Build a function that models a relationship between two quantities.

Extend the domain of trigonometric functions using the unit circle.

Build new functions from existing functions.

Define, evaluate, and compare functions.

Construct and compare linear and exponential models and solve problems.

Model periodic phenomena with trigonometric functions.

Use functions to model relationships between quantities.

Understand the concept of a function and use function notation.
problem_activity: Task
Katy is told that the cost of producing $x$ DVDs is given by $C(x) = 1.25x + 2500.$ She is then asked to find an equation for $\frac{C(x)}{x}$, the average cost per DVD of producing $x$ DVDs.
She begins her work: $$\frac{C(x)}{x} =\frac {1.25x+2500}{x}$$ and finishes by simplifying both sides to get: $$C = 1.25+\frac{2500}{x}$$  Is Katy's answer correct? Explain.


correct_option_index: 11