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:

Step1: Analyze the division

First, calculate \( \frac{1650}{33.33} \). Let's approximate \( 33.33 \approx \frac{100}{3} \), so \( \frac{1650}{\frac{100}{3}} = 1650\times\frac{3}{100}= 49.5 \).

Step2: Evaluate the mistake

Zach got 50 bundles, but the actual division (approximate) gives 49.5, and he also has an extra bundle (but the problem is about the calculation of needed bundles). The key is whether he checked if 50 makes sense. Since \( 33.33\times50 = 1666.5 \), which is more than 1650, and he has less than one bundle left, but the main mistake is not verifying if 50 is reasonable. Alternatively, the division error: if we do \( 1650\div33.33 \approx 49.5 \), so when he divided 1650 by 33.33, he made an error (like miscalculating the division, getting 50 instead of ~49.5). Wait, but let's check the options. Option D says he didn't ask if 50 makes sense. But let's re - examine:

Wait, the roof is 1650 sq ft, each bundle is 33.33 sq ft. So number of bundles needed is \( 1650\div33.33\approx49.5 \). He decided he needs 50 bundles. But at the end, he has less than one full bundle left. Wait, maybe the mistake is in the division. Let's calculate \( 33.33\times50 = 1666.5 \), which is 16.5 sq ft more than 1650. But he has less than one bundle left. Wait, the options:

Option A: Rounding. But 33.33 is a decimal, maybe he should have rounded the number of bundles up, but the main issue is the division.

Option C: Error in dividing 1650 by 33.33. Because \( 1650\div33.33\approx49.5 \), not 50. So he made an error in division.

Wait, let's recalculate \( 1650\div33.33 \):

\( 33.33\times49 = 33.33\times50 - 33.33=1666.5 - 33.33 = 1633.17 \)

\( 1650 - 1633.17 = 16.83 \)

\( 16.83\div33.33\approx0.505 \)

So total is \( 49 + 0.505\approx49.505 \), so approximately 50 (rounding up). But he has less than one bundle left. Wait, the problem says "which calculation mistake did Zach MOST LIKELY make?".

Wait, the options:

A: Not rounding correctly. But 49.5 rounded up is 50, so maybe not.

B: Not ordering extra bundle. But he did order an extra bundle? No, the problem says "plus one extra bundle in case...", but he determined he needs 50 bundles. Wait, no, the "plus one extra" is separate? Wait, the problem says "Zach will buy shingles in 33.33 square foot bundles, plus one extra bundle in case... For this project, he divides 1,650 by 33.33 and determines he needs 50 bundles of shingles."

Wait, maybe the mistake is in the division. Let's do \( 1650\div33.33 \):

\( 33.33\times50 = 1666.5 \), which is more than 1650. So when he divided 1650 by 33.33, he made an error (he should have gotten approximately 49.5, not 50). So option C: Zach made an error dividing 1,650 by 33.33.

Step3: Confirm the answer

Since \( 1650\div33.33\approx49.5 \), and he got 50, so the division was wrong. So the answer is C.

Answer:

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