Answer to Question #217668 in Discrete Mathematics for Anonymous

Question

In a school 844 students have access to three software packages A, B, C.

Where 743 didn’t use any software, 740 used only package C, 742 used only package

A,741 used package B, 739 used all three packages, 738 used both A and C

a) Draw a Venn diagram with all sets enumerated as for as possible.

b) If twice as many students used package A as Package C, write down a pair

of simultaneous equations in x and y.

c) Solve these equation to find x and y.

d) How many students used package B.

Answer 1

a)

$$26+7+8+3+x+y+10+28=100$$

b)

$$26+x+3+10=2(8+3+y+10)$$

Then

$$\begin{matrix} x+y=18\\ \\ x+39=2y+42 \end{matrix}$$

c)

$$\begin{matrix} x=18-y\\ 18-y+39=2y+42 \end{matrix}$$ $$\begin{matrix} x=18-y\\ 3y=15 \end{matrix}$$ $$\begin{matrix} x=13\\ y=5 \end{matrix}$$

d)

$$7+13+5+10=35$$

35 students used package B.