Final answer:
Hence, without complete accuracy in the provided details, option c still seems like the intended correct choice given the context.
Step-by-step explanation:
The question asks how many shells in the Richardson family's collection are neither conch shells nor cockle shells. Given that 13 of the shells are cockle shells and they constitute 60% of the shell collection, we can deduce the number of cockle and conch shells and then find out how many are of other types. First, let's find the total number of cockle and conch shells. If 13 cockle shells account for 60%, then the total number of shells that are either cockle or conch (let's call this number X) can be represented as 13 = 0.6X. Dividing 13 by 0.6 gives us X = 21.67, which we can round to 22 since we can't have a fraction of a shell. Therefore, there are 22 shells that are cockle or conch.
Next, we subtract the total number of cockle and conch shells (22) from the entire collection (75). So, 75 - 22 gives us 53 shells that are neither cockle nor conch. However, since this number was not presented as an option and we made an assumption due to rounding during calculation, we may consider the error and check the available choices. Looking at the options, the closest and only sensible choice that falls below our calculated 53 shells is option c, which is 29 shells. While it doesn't match our calculated number, it's possible the question has a mistake, and option c seems to be the intended answer because options b and d exceed 53, and option a corresponds to the number of cockle shells given in the question itself, which is not what we are looking for.
Alternatively, the question might have intended to say that the 13 cockle shells constitute 60% of the non-conch shells in the collection, which would make a different calculation. In this case, if 13 cockle shells constitute 60% of the non-conch shells, then the number of non-conch shelves is 13 / 0.6 = 21.67, approximately 22 non-conch shells. Subtracting the number of cockle shells from this total (22 - 13) would give us 9 additional non-conch, non-cockle shells, but this is not an available answer choice, potentially indicating an error in phrasing or details provided in the question. The question appears to have a discrepancy in provided details, but implies finding the number of seashells that are neither conch shells nor cockle shells in a given collection. While initial calculations suggest there are 53 seashells that aren't cockle or conch shells, option c, which indicates 29 shells, seems to be the intended answer choice provided by the student, possibly due to a typo or error in the question itself.