Question

At a football match one day , there were 55 men more than women . The number of children was twice the number of women and the number of men was twice the number of women and children combined . How many people were at the match .

Answer 1

Given:

• Number of men is 55 more than women.
• Number of children is twice the number of women.
• Number of men is also equal to twice the number of children and women combined together.

Solution:

Let the number of women be x. Then,

Number of men = (x + 55)

And number of children = 2x

Number of men is twice the number of women and children combined. [given]

Twice the sum of number of children and women = 2 (2x + x)

                                                                                   = 2 × 3x

                                                                                   = 6x

As (x + 55) = 6x, we can create an equation as follows:

$\because \sf{6x = x+55}\\\implies \sf{6x - x = 55}\\\implies \sf{5x = 55}\\\implies \sf{x = \dfrac{55}{5}}\\\implies \sf{x = 11}$

As, value of x = 11

Therefore, Number of women = x = 11

Number of men = x + 55 = 11 + 55 = 66

Number of children = 2x = 2 × 11 = 22

Total number of people at the match = (11 + 66 + 22)

                                                              = 99

Hence, total number of people at the match is 99.