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A department store surveyed 428 shoppers, and the following information was obtained: 217 shoppers made a purchase, and 294 were satisfied with the service they received. If 50 of those who made a purchase were not satisfied with the service, how many shoppers did the following?(a) made a purchase and were satisfied with the service(b) made a purchase or were satisfied with the service(c) were satisfied with the service but did not make a purchase(d) were not satisfied and did not make a purchase

Question

A department store surveyed 428 shoppers, and the following information was obtained: 217 shoppers made a purchase, and 294 were satisfied with the service they received. If 50 of those who made a purchase were not satisfied with the service, how many shoppers did the following?(a) made a purchase and were satisfied with the service(b) made a purchase or were satisfied with the service(c) were satisfied with the service but did not make a purchase(d) were not satisfied and did not make a purchase

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Solution

(a) To find the number of shoppers who made a purchase and were satisfied with the service, we start with the total number of shoppers who made a purchase (217) and subtract those who were not satisfied (50). So, 217 - 50 = 167 shoppers made a purchase and were satisfied with the service.

(b) To find the number of shoppers who either made a purchase or were satisfied with the service, we add the total number of shoppers who made a purchase (217) to the total number of shoppers who were satisfied (294). However, this would count the shoppers who both made a purchase and were satisfied twice, so we need to subtract the number we found in part (a). So, 217 + 294 - 167 = 344 shoppers either made a purchase or were satisfied with the service.

(c) To find the number of shoppers who were satisfied with the service but did not make a purchase, we start with the total number of shoppers who were satisfied (294) and subtract those who made a purchase and were satisfied (167). So, 294 - 167 = 127 shoppers were satisfied with the service but did not make a purchase.

(d) To find the number of shoppers who were not satisfied and did not make a purchase, we start with the total number of shoppers (428) and subtract those who either made a purchase or were satisfied (344). So, 428 - 344 = 84 shoppers were not satisfied and did not make a purchase.

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