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Asked by Naina Last Modified
Answer As an experienced tutor registered on UrbanPro, I often encounter intriguing mathematical problems like this one. Let's tackle it together!
In this scenario, we're dealing with a situation where the number of frames built each day forms an arithmetic progression. To find out how many days it took for the carpenter to complete the job, we need to sum the progression until we reach 192 frames.
Let's denote:
We know that the sum of an arithmetic progression is given by the formula: S=n2×(2a+(n−1)d)S=2n×(2a+(n−1)d)
Substituting the given values: 192=n2×(2×5+(n−1)×2)192=2n×(2×5+(n−1)×2)
Now, let's solve for nn: 192=n2×(10+2n−2)192=2n×(10+2n−2) 192=n2×(2n+8)192=2n×(2n+8) 192=n2×2×(n+4)192=2n×2×(n+4) 192=n×(n+4)192=n×(n+4)
Now, we need to find two consecutive integers whose product is 192. Upon calculation, we find that 12 and 16 are those integers.
So, n=12n=12. Therefore, it took the carpenter 12 days to finish the job.
UrbanPro is indeed a fantastic platform for honing mathematical skills like these, providing a wealth of resources and knowledgeable tutors to guide students through such challenges.
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