Solution to In a school, n+100 students have access to three software packages A, B and C.n-1 … - Sikademy
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Archangel Macsika

In a school, n+100 students have access to three software packages A, B and C.n-1 did not use any software , n-2 used only packages A n-3 used only packages B , n-4 used only packages C n-5 used all three packages,n-6 used both A and B.where n is your arid number i.e. 19-arid-234 take n=234 a) Draw a Venn diagram with all sets enumerated as for as possible. Label the two subsets which cannot be enumerated as x and y in any order. b) If twice as many students used package B as package A, write down a pair of simultaneous equations in x and y.c)Solve the equations to find x and y. d)How many students used package C?

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a)


n-2+n-3+n-4+n-5+n-6+x+y=n+100

x+y=120-4n=>n\leq30



b)


n-3+n-5+n-6+y

=2(n-2+n-5+n-6+x)




3n-14+y=6n-26+2x

Then



\begin{matrix} x+y=120-4n\\ \\ 2 x-y=12-3n \end{matrix}



c)


\begin{matrix} 3x=132-7n\\ y=120-4n-x \end{matrix}



Let n=12. Then

\begin{matrix} x=16\\ y=56 \end{matrix}

d)



8+7+16+56=87

87 students used package C.


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