Out of 124

Out of 124 students, 68 students went on at least one of the two trips. 82 students did not go on the first trip, and 63 students went on just one trip. How many students went only on the first trip, and how many students went on the second trip?

Correct answer:

x =  49
b =  19

Step-by-step explanation:

$$\begin{gathered} n=124 \\ A\cup B=68 \\ {A}^{\prime }=82 \\ A\cup B-A\cap B=63 \\ m=n-68=124-68=56 \\ n=m+x+y+z \\ 82=n-m+z \\ z=82+m-n=82+56-124=14 \\ 63=x+z \\ x=63-z=63-14=49 \\ y=n-m-x-z=124-56-49-14=5 \end{gathered}$$

$b=y+z=5+14=19$

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