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, in json format:
{
  "explanation": "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: Work with addition and subtraction equations.

Understand the relationship between zeros and factors of polynomials.

Solve systems of equations.

Analyze patterns and relationships.

Understand and apply properties of operations and the relationship between addition and subtraction.

Rewrite rational expressions.

Create equations that describe numbers or relationships

Represent and solve problems involving multiplication and division.

Understand properties of multiplication and the relationship between multiplication and division.

Understand the connections between proportional relationships, lines, and linear equations.

Represent and solve problems involving addition and subtraction.

Write and interpret numerical expressions.

Reason about and solve one-variable equations and inequalities.

Multiply and divide within 100.

Use polynomial identities to solve problems.

Use the four operations with whole numbers to solve problems.

Perform arithmetic operations on polynomials.

Work with radicals and integer exponents.

Interpret the structure of expressions.

Use properties of operations to generate equivalent expressions.

Add and subtract within 20.

Write expressions in equivalent forms to solve problems.

Represent and solve equations and inequalities graphically.

Solve equations and inequalities in one variable.

Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.

Generate and analyze patterns.

Solve problems involving the four operations, and identify and explain patterns in arithmetic.

Represent and analyze quantitative relationships between dependent and independent variables.

Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

Gain familiarity with factors and multiples.

Analyze and solve linear equations and pairs of simultaneous linear equations.

Apply and extend previous understandings of arithmetic to algebraic expressions.

Work with equal groups of objects to gain foundations for multiplication.

Understand solving equations as a process of reasoning and explain the reasoning.
problem_activity: Task
A theme park has a log ride that can hold 12 people. They also have a weight limit of 1500 lbs per log for safety reasons. If the average adult weighs 150 lbs, the average child weighs 100 lbs and the log itself weighs 200, the ride can operate safely if the inequality
$$ 150A + 100C + 200 \leq 1500 $$
is satisfied ($A$ is the number of adults and $C$ is the number of children in the log ride together). There are several groups of children of differing numbers waiting to ride. Group one has 4 children, group two has 3 children, group three has 9 children, group four 6 children while group five has 5 children.
If 4 adults are already seated in the log, which groups of children can safely ride with them?


correct_option_index: 12