Final answer:
The height of the pile after three weeks is 43 1/2 inches, which is calculated by adding the initial height of 17 3/4 inches to three times the weekly increase of 8 7/12 inches. It appears there is no matching option in the given choices.
Step-by-step explanation:
The student is asking about the height of a pile of books in Mr. Halpert's math class after three weeks, given that the initial height is 17 3/4 inches and it increases weekly by 8 7/12 inches. To solve this, let's add the weekly increase to the initial height for three weeks:
- Initial height: 17 3/4 inches
- Weekly increase: 8 7/12 inches
- Total increase over three weeks: 3 × 8 7/12 inches
To calculate the total increase over three weeks, convert both measurements to improper fractions to make the addition simpler:
- 17 3/4 inches = 71/4 inches
- 8 7/12 inches = 103/12 inches
- Total increase over three weeks = 3 × (103/12) inches = 309/12 inches
Now add the total increase to the initial height:
- 71/4 + 309/12
- To add these, find a common denominator, which is 12:
- 213/12 + 309/12 = 522/12 inches
- 522/12 inches can be simplified to 43 1/2 inches
Therefore, the height of the pile after three weeks is 43 1/2 inches, which is not an option provided. Thus, there's likely an error in the options given or the student must recheck their given answer choices. This answer is based on the mathematics of addition and understanding of fractions.