Christmas or Easter

Please calculate this example by the Venn equation. They asked 73 students whether they liked Christmas or Easter. Thirty-four of them like one of the holidays. 39 loves Easter. There are twice as many students who wish for both holidays as those who only love Easter. How many students only like Christmas (a =)? How many students do not like any of the holidays (b =)?

Correct answer:

a =  21
b =  13

Step-by-step explanation:

73 = a + b + 39
34 = a + 39 - c
c = 2·(39-c)

a+b = 34
a-c = -5
3c = 78

Row 2 - Row 1 → Row 2
a+b = 34
-b-c = -39
3c = 78


c = 78/3 = 26
b = -39+c/-1 = -39+26/-1 = 13
a = 34-b = 34-13 = 21

a = 21
b = 13
c = 26

Our linear equations calculator calculates it.

$b=13$

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