LEARN · EXPLAIN · REVISE

A budget is 17 and each item costs 5. Find the greatest number of whole items affordable.

Read the idea, work independently, then explain what changed.

高一必修第一册(A版).pdf · 3.4 · PDF 100 / printed page 93

TOPIC 01

Applications of functions I

Build understanding of applications of functions i through definitions, contrasting cases and justified applications.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Standard#Your turn

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Define the variable and its units, form a model, and check feasible inputs.

Hint 2

Round the continuous upper bound down, not to the nearest integer.

Worked solution

Define the variable and its units, form a model, and check feasible inputs.
Calculate or simplify this relation.
$5n\le17;\quad n\in\mathbb Z_{\ge0};\quad n_{\max}=3$
A rounded-up purchase would exceed the budget.

The requested value is 3.

Checks and common pitfalls: A rounded-up purchase would exceed the budget.

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Expected reasoning: State variables, units, assumptions and feasible inputs.
Expected reasoning: A fitted formula needs contextual checks and further evidence.
Expected correction: Average speed is not generally the average of two speeds.