Calculate a constrained weighted score

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: Score equals two times reliability rating plus efficiency rating. Formula: 2*a+b. Variable key: a = reliability rating, b = efficiency rating
• Distinct worked inputs and result: A distinct model has reliability 3 and efficiency 2: 2×3+2=8 points.
• Assessment case 1: Supplied case 1: reliability rating=4; efficiency rating=3, using the explicitly named quantities. Score equals two times reliability rating plus efficiency rating. What result follows?
• Assessment case 2: Supplied case 2: reliability rating=3; efficiency rating=5, using the explicitly named quantities. Score equals two times reliability rating plus efficiency rating. What result follows?
• Assessment case 3: Supplied case 3: reliability rating=5; efficiency rating=2, using the explicitly named quantities. Score equals two times reliability rating plus efficiency rating. What result follows?
• Assessment case 4: Supplied case 4: reliability rating=2; efficiency rating=4, using the explicitly named quantities. Score equals two times reliability rating plus efficiency rating. What result follows?
• Assessment case 5: Supplied case 5: reliability rating=4; efficiency rating=5, using the explicitly named quantities. Score equals two times reliability rating plus efficiency rating. What result follows?
• Assessment case 6: Supplied case 6: reliability rating=5; efficiency rating=4, using the explicitly named quantities. Score equals two times reliability rating plus efficiency rating. What result follows?

Learn the idea

A weighted score combines specified criteria after essential constraints are checked. Weights express priorities, not objective proof of a universally best design. Supplied ratings have the same stated scale.

Score equals two times reliability rating plus efficiency rating. The formula in the supplied model is 2*a+b. Variable key: a = reliability rating, b = efficiency rating. Apply the specified weight to the correct criterion. Check essential constraints before scoring.

A distinct model has reliability 3 and efficiency 2: 2×3+2=8 points. Different weights can change rankings. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

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Take it further

Changed-input task: use the same stated model with reliability rating=5; efficiency rating=3. Expected result: 13 score points. Explain what changes and keep this assumption: Different weights can change rankings.

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