Question

At a soccer ,match 60% of the spectator were men and rest are women and childre.

Answer 1

Answer:

s = 700

Step-by-step explanation:

We need a series of equations to be able to sub back and forth into one another in order to get this down to one variable, s for spectators.  This is what we know from the info (in algebraic expression/equation form):

6s = men (60% of the spectators are men)

4s = women + children (40% of the spectators are women and children)

# of children = 2/3 women

# of men = women + 252 (There are 252 more men than women) and

# women = men - 252

Those are the equations we need to solve for the number of spectators.

Start at the top with

6s = men.  We know that the number of men = women + 252, so

6s = women + 252.

4s = women + children. We know that the number of children is 2/3 the number of women, so

4s = women + 2/3 women.  If the number of men = women + 252, then

4s = men - 252 + 2/3(men - 252) which simplifies to

4s = 3/3 men - 252 + 2/3 men - 168 and

4s = 5/3 men - 420 and

4s = s - 420 and

6s = -420 so

s = 700

Answer 2

Although your answer is incomplete, you may be referring to:

At a soccer match, 60% of the spectators are men and the rest are women and children. The number of children is 2/3 of the women. There are 252 more men than women at the soccer match. How many spectators are there altogether?

Given:

Percentage of men = 60%

Percentage of women and children = 40%

Number of children = $\frac{2}{3}$ the number of women

Number of men = 252 more than the number of women

To Find:

The total number of spectators

Let us assume:

Let the number of men be x

Let the number of women be y

Let the number of children be z

Let the total number of spectators be a

Solution:

• For solving this question, we need to make equations based on the given conditions.

Step 1: Find a relation between the number of women and children

• It is given that the number of children = $\frac{2}{3}$ the number of women

                                        ⇒ z = $\frac{2}{3}$ y

• We also know that the total number of women and children makes up 40% of the total number of spectators.

                       ⇒ y + z = $\frac{40}{100}$ × a

                       ⇒ y + $\frac{2}{3}$y = $\frac{2}{5}$a

                       ⇒ $\frac{5y}{3}$ = $\frac{2a}{5}$

                       ⇒ y = $\frac{6a}{25}$                                      (1)

Step 2. Find an expression for the relation between the number of men and women.

• We know that the number of men is 252 more than the number of women.

                                     x = y + 252

                                ⇒ x-y = 252

• We also know that the number of men makes up 60% of the total number of spectators.

                                         

                                          ⇒ x = $\frac{60}{100}$ × a

                                          ⇒ x = $\frac{3a}{5}$                           (2)

Step 3. Find the total number of spectators.

• From (1) and (2) we get:

                         x-y = 252 can be written as:

                               $\frac{3a}{5}$ - $\frac{6a}{25}$ = 252

                          ⇒ $\frac{15a - 6a}{25}$ = 252

                          ⇒ $\frac{9a}{25}$ = 252

                          ⇒ a = 700

Thus, the total number of spectators is 700.