Systems in Context

Learn and apply systems in context using equations, examples, and interpretation.

Lesson 5 of 53 parts Practice Flashcards

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Defining Two Variables

Objective: Explain and use defining two variables in an Algebra 1 problem.

A contextual system may use variables for two related unknowns, with units and restrictions stated before solving. It prevents confusing prices with item counts.

Worked examples

Try itExample 1.1: 5 adult tickets at $2 each and one child ticket at $13 cost how much?Show answer

23. Multiply ticket counts by their prices, then add. The answer is 23.

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Defining Two Variables

Objective: Explain and use defining two variables in an Algebra 1 problem.

A contextual system may use variables for two related unknowns, with units and restrictions stated before solving. It prevents confusing prices with item counts.

Worked examples

Try itExample 1.1: 5 adult tickets at $2 each and one child ticket at $13 cost how much?Show answer

23. Multiply ticket counts by their prices, then add. The answer is 23.

Writing Independent Constraints

Objective: Explain and use writing independent constraints in an Algebra 1 problem.

Each equation should express a different relationship, such as total count and total cost, for the same unknown quantities. A pair may fit one story detail but not the other.

Worked examples

Try itExample 2.1: 8 adult tickets at $3 each and one child ticket at $23 cost how much?Show answer

47. Multiply ticket counts by their prices, then add. The answer is 47.

Feasible Solutions

Objective: Explain and use feasible solutions in an Algebra 1 problem.

After solving, require meaningful answers such as nonnegative integer ticket counts and consistency with the original totals. No, unless the problem explicitly gives another meaning.

Worked examples

Try itExample 3.1: 11 adult tickets at $4 each and one child ticket at $33 cost how much?Show answer

77. Multiply ticket counts by their prices, then add. The answer is 77.

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