43. According to the plan, 70 pounds of candy will be produced during the first week and the amount of candy produced during each week after the first will be 2 pounds greater than the amount produced during the preceding week. What will be the total amount of candy produced during the first 6 weeks?
Answer: D
The total amount of candy produced during the first 6 weeks is 450 pounds.
The total amount of candy produced over the first 6 weeks can be calculated by recognizing the pattern in production. Starting with 70 pounds in the first week, each subsequent week increases by 2 pounds, leading to a total of 450 pounds after 6 weeks.
A) 80
This option is incorrect as it does not reflect the calculated total of candy production over the 6 weeks. The production increases weekly, making 80 pounds an insufficient total.
B) 140
This option is also incorrect. While it might consider a smaller subset of the production, it fails to account for the increase in production each week, resulting in a total far less than what has been calculated.
C) 420
This option is incorrect as well. Although it is a large number, it does not align with the calculated total of 450 pounds. The weekly increments lead to a larger cumulative total than 420.
D) 450
This is the correct option. The weekly production follows an arithmetic sequence: 70, 72, 74, 76, 78, and 80 pounds, summing up to 450 pounds over the 6 weeks.
E) 600
This option is incorrect. A total of 600 pounds exceeds the calculated production total based on the weekly increases.
Conclusion
The correct answer of 450 pounds accurately reflects the sum of candy produced over the 6 weeks, taking into account the consistent increase of 2 pounds each week. All other options fail to represent the arithmetic progression of production correctly, resulting in totals that are either too low or excessively high.