Question

In a school, 100 students have access to three software packages a, b and c.

28 did not use any software
8 used only packages a
26 used only packages b
7 used only packages c
10 used all three packages 13 used both a and b

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 these equations to find x and y.

d.) How many students used package C?​

Answer 1

Hi,

Explanation:

a) see attached picture

b)

A=8+3+10+x=x+21

B=3+10+26+y=y+39

B=2A => y+39=2x+42 => 2x-y=-3

Nb students=100 => 8+3+10+x+26+y+7+28=100 => x+y=18

`\left\{\begin{array}{ccc}2x-y&=&-3\\x+y&=&18\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}3x&=&15\\x+y&=&18\\\end{array}\right.\\\\\\\left\{\begin{array}{ccc}x&=&5\\y&=&13\\\end{array}\right.\\`

d)

x+y+10+7=5+13+17=35