A survey of 255 adults found that during the last year, 40 traveled by plane but not by train, 75 traveled by train but not by plane, 50 traveled by bus but not by plane or by train, 55 traveled by bus and plane, 35 traveled by all three, and 170 traveled by plane or train. How many did not travel by any of these modes of transportation?

Question

Jean

Mathematics

20 March, 03:26

A survey of 255 adults found that during the last year, 40 traveled by plane but not by train, 75 traveled by train but not by plane, 50 traveled by bus but not by plane or by train, 55 traveled by bus and plane, 35 traveled by all three, and 170 traveled by plane or train. How many did not travel by any of these modes of transportation?

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Efrain Morris · Answer 1

35 people did no travel by any of those modes of transportation.

Step-by-step explanation:

Reviewing the groups described, we can see there are 170 that traveled by either plane or train and 50 traveled by bus, but not plane or train.

This means that the 50 people that traveled by bus are not included in the group of 170 that used either plane or train.

Since those two groups include people that used bus (50 people) and people that used either plane or train (170 people), the union of these two sets include all the people that used at least one of the tree modes of transportation mentioned (bus, plane or train).

The result of the union between these two sets is 50+170=220 people which travel by at least one of those modes of transportation.

Since the total number of surveyed adults is 255, the number of people that did not travel by any of these modes of transportations is 255-220=35 people.