Question

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?

Answer 1

Answer:

35 adults did not travel by any of these modes of transportation

Step-by-step explanation:

I add a drawing of the sets

Let's write the equations system reading the exercise :

$A+B+C+D+E+F+G+H=255\\B+E=40\\C+F=75\\D=50\\E+G=55\\G=35\\B+C+E+F+G+H=170$

We must find A.

We solve the system equations :

$E+G=55\\G=35\\Then\\E+35=55\\E=20$

$B+E=40\\E=20\\Then\\B+20=40\\B=20$

$B+C+E+F+G+H=170\\B=20\\E=20\\G=35\\C+F=75$

$B+(C+F)+E+G+H=170\\20+75+20+35+H=170\\H=20$

$A+B+C+D+E+F+G+H=255\\A+B+(C+F)+D+E+G+H=255\\A+20+75+50+20+35+20=255\\A=35$