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Reading & writing · Grades 9–12

The cheaper proposal

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The cheaper proposal

A headline said that Proposal B would cost 20% less than Proposal A. The detailed table showed that A included equipment, installation and five years of maintenance, while B listed equipment and installation only. Both arithmetic totals were correctly added, but they covered different things. The review group requested a common five-year cost comparison and kept uncertain maintenance estimates visible. After the missing category was included, B still appeared cheaper, though by a much smaller margin. The headline had been numerically neat but incomplete.

Try it yourself

  1. What was the main problem with the initial cost comparison?

    1. A percentage can never be calculated.
    2. Neither proposal included equipment.
    3. Both additions were necessarily wrong.
    4. The totals included different categories.

  2. Why can correct arithmetic still support a misleading headline?

  3. What common basis did the review group request?

    1. five-year costs including comparable categories
    2. only the proposal titles
    3. only equipment colour
    4. the number of pages

  4. Why keep uncertain estimates visible?

  5. What happened after the missing category was included?

    1. B was guaranteed to be free.
    2. B still appeared cheaper, but by less.
    3. No comparison could ever be made.
    4. A became identical to B in every respect.

  1. Rewrite the headline's claim more cautiously without inventing a new percentage.

Answers and marking notes

Answers and marking notes
  1. The totals included different categories.

    The accounting boundaries were inconsistent.

  2. The inputs or categories may not be comparable, so an accurate calculation answers an incomplete question.

    Credit scope as well as numerical correctness.

  3. five-year costs including comparable categories

    The same time horizon and scope support comparison.

  4. Readers need to see assumptions and possible variation rather than treating estimated values as exact.

    Credit transparency about uncertainty.

  5. B still appeared cheaper, but by less.

    The passage explicitly retains a smaller apparent saving.

  6. On a comparable five-year estimate, B appears cheaper, with the size of the saving depending on maintenance assumptions.

    Credit consistent scope and uncertainty; do not invent a numerical result.

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