Equation Word Problems

Learn and apply equation word problems using equations, examples, and interpretation.

Lesson 5 of 53 parts Practice Flashcards

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Defining the Unknown

Objective: Explain and use defining the unknown in an Algebra 1 problem.

Assign a variable to a quantity and unit before translating a verbal relationship into an equation. They make the model interpretable.

Worked examples

Try itExample 1.1: A fixed fee is $13 plus $2 per item. How many items cost $23?Show answer

5. Subtract the $13 fee and divide by the $2 rate. The answer is 5.

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Defining the Unknown

Objective: Explain and use defining the unknown in an Algebra 1 problem.

Assign a variable to a quantity and unit before translating a verbal relationship into an equation. They make the model interpretable.

Worked examples

Try itExample 1.1: A fixed fee is $13 plus $2 per item. How many items cost $23?Show answer

5. Subtract the $13 fee and divide by the $2 rate. The answer is 5.

Fixed Fees and Rates

Objective: Explain and use fixed fees and rates in an Algebra 1 problem.

A linear cost model C=rm+b combines a rate r per item, count m, and fixed fee b; all amounts must use compatible units. The rate times the number of items.

Worked examples

Try itExample 2.1: A fixed fee is $23 plus $3 per item. How many items cost $47?Show answer

8. Subtract the $23 fee and divide by the $3 rate. The answer is 8.

Contextual Reasonableness

Objective: Explain and use contextual reasonableness in an Algebra 1 problem.

A numerical solution must satisfy both the equation and restrictions such as nonnegative distance and whole-item counts. An item count cannot be negative in this context.

Worked examples

Try itExample 3.1: A fixed fee is $33 plus $4 per item. How many items cost $77?Show answer

11. Subtract the $33 fee and divide by the $4 rate. The answer is 11.

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