Question

zach is buying materials to cover a 1,650 square foot roof with shingles. zach will buy shingles in 33.33 square foot bundles, plus one extra bundle in case some shingles break or the roof measurements are not exact. for this project, he divides 1,650 by 33.33 and determines he needs 50 bundles of shingles. at the end of the project, he has less than one full bundle of shingles left. which calculation mistake did zach most likely make? a) zach did not round correctly when determining the number of bundles needed. b) zach did not order the extra bundle. c) zach made an error dividing 1,650 by 33.33. d) zach did not ask himself if 50 bundles made sense.

Explanation:

Step 1: Analyze the division

To find the number of bundles needed, we calculate $\frac{1650}{33.33}$. Let's do this division: $1650\div33.33\approx49.5$ (since $33.33\times49.5 = 33.33\times(50 - 0.5)=33.33\times50-33.33\times0.5 = 1666.5 - 16.665 = 1649.835$, which is close to 1650). But Zach got 50.

Step 2: Check the options

• Option A: Rounding 49.5 to 50 is a reasonable round (since we can't buy a fraction of a bundle, we round up). So this is not the mistake.
• Option B: He did order an extra bundle (he considered one extra), so this is not the mistake.
• Option C: The error here is in the division. When he divided 1650 by 33.33, he should have gotten approximately 49.5, but he got 50. So this is the calculation error in division.
• Option D: 50 bundles do make sense (since we round up), so this is not the mistake.

Answer:

C) Zach made an error dividing 1,650 by 33.33.