Answer:
a) 24
b) 60
c) x = 2
d) 10
Step-by-step explanation:
a) The student who don't like to play any of the games is given as the complement inside the universal set. This value is 24 noted at the bottom left of the diagram.
b) The amount of students who like playing football can be summed up by adding the values in the circles of F.
These are 54-2x + x + 6 + x. Note that the positive and negative x-terms in this expression cancel eachother, leaving only 54 + 6 = 60.
c) To find x we must sum up all values inside the circles (only once) as well as the complement, and then subtract this value from the total number of students which is given as 126 in the description.
126 = 24 + (54 - 2x) + x + 6 + x + x + (34 - 2x) + (14 - 2x)
In the above equation I have tried to group best I can the values. We now solve this equation.
[tex]126 = 132 - 3x \implies \\3x + 126 - 126 = 132 - 126 - 3x + 3x \implies\\ 3x = 6 \implies\\\frac{3x}{3} = \frac{6}{3} \implies\\x = 2[/tex]
d) The student who only like playing tennis is given by the equation 14 - 2x.
With x = 2 this equation can be read as 14 - 2*2 = 14-4 = 10
If you have any questions about this explanation, just leave a comment. :)
