Question

: At a Pokemon award ceremony there are three types of medals to be awarded: Leader, Champion, and Ranger. There are 48 awardees present in total, including 19 Leader medal winners, 27 Champion medal winners, and 25 Ranger medal winners. For any two types of medals, the number of people who won these two medals is the same. There are 4 people who won all three medals. How many people won exactly two medals

Answer 1

The correct answer is "
`a+b+c=15`".

Explanation:

The figure according to the given question is attached below.

Given that,

Number of people,

p = 4

Let the suitable notations are:

a, b, c, x, y, z and p

where,

Only leader M = x

Only champion M = y

Only range M = z

Exactly two medals = a+b+c

All three medals = p

The equations will be:

`x+a+b+p=19`...(1)

`y+a+c+p=27`...(2)

`z+b+c+p=25`...(3)

`x+y+z+a+b+c+p=48`...(4)

Now,

From equation (1), (2) and (3), we get

`x+y+z+2(a+b+c)+3p=71`

`x+y+z+2(a+b+c)=71-12`

`x+y+z+2(a+b+c)=59`...(5)

By applying subtraction between equation (5) and (4), we get

`a+b+c-p=59-48`

`a+b+c=4+11`

`a+b+c=15`