Four carpenters each built an average of 42 chairs last week. If no chairs were left uncompleted, and if Peter, who built 50 chairs, built the greatest number of chairs ,what is the least number of chairs one of the carpenters could have built, if no carpenter built a fractional number of chairs?

They built a total of 42*4=168 chairs.

Peter built 50 chairs, (the most),
Paul built 49 (most below 50)
Mary built 49 (most below 50)
So
Lent built 150-50-49-49=20 chairs.

To find the least number of chairs one of the carpenters could have built, we need to consider the scenario where Peter, who built 50 chairs, built the greatest number of chairs.

If the average number of chairs built by four carpenters is 42, then the total number of chairs built by all four carpenters is 42 * 4 = 168 chairs.

If Peter built the greatest number of chairs, and no chairs were left uncompleted, then the sum of the chairs built by the other three carpenters must be equal to 168 - 50 = 118 chairs.

Since we want to find the least number of chairs one of the carpenters could have built, we need to distribute the remaining 118 chairs as evenly as possible among the three carpenters.

Dividing 118 by 3 gives us an average of about 39.333 chairs per carpenter.

Since we cannot have a fractional number of chairs for each carpenter, we need to round down the average to the nearest whole number.

So, the least number of chairs one of the carpenters could have built is 39 chairs.

To find the minimum number of chairs one of the carpenters could have built, we need to consider the given information.

We know that Peter built the greatest number of chairs, which is 50. The average number of chairs built by each carpenter is given as 42. If we assume all four carpenters built exactly 42 chairs each, the total number of chairs built would be 4 * 42 = 168.

Since Peter built 50 chairs and the total number of chairs built is 168, the remaining three carpenters must have built a total of 168 - 50 = 118 chairs.

To find the minimum number of chairs one of the three remaining carpenters could have built, we can distribute the remaining 118 chairs evenly among them. Since we want to find the minimum, we assume the most uneven distribution.

If we assume one carpenter built one less chair than the other two, then the number of chairs built by the remaining three carpenters would be divided as follows: (118 - 1) / 3 = 39 chairs each.

Therefore, the minimum number of chairs one of the carpenters could have built, if no carpenter built a fractional number of chairs, is 39.