Answer to Question #208519 in Discrete Mathematics for Zam

Question

In a school 100 students have access to three software packages A, B, C.

Where 28 didn’t use any software, 8 used only package C, 26 used only package 

A,7 used package B, 10 used all three packages, 13 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.