At a concert, 2/5 of the people were men. there were 3 times as many women as children. if there were 45 more men than children, how many people were there at the concert?

Total number of people=225

Step-by-step explanation:

The total number of each group of people can be expressed as;

Total number of men (m)=(2/5)×total number of people (p)

m=(2/5)p...equation 1

Total number of women (w)=3×total number of children (c)

w=3 c...equation 2

Total number of men (m)=Total number of children (c)+45

m=c+45...equation 3

The total number of people (p)=Number of women (w)+number of children (c)+number of men (m)

where;

Number of women (w)=3 c

Number of children (c)=c

Number of men (m)=c+45

replacing;

The total number of people (p)=3 c+c+(c+45)

p=4 c+45

The total number of people can be expressed as;

p=4 c+45

since the total number of men (m)=(2/5)p

m=2/5(4 c+45)=(8/5) c+18equation 4

Equating equation 4 to equation equation 3

(8/5) c+18=c+45

(8/5) c-c=45-18

(3/5) c=27

c=27×5/3

c=45

Total number of people, p=4 c+45

replacing with c=45

p=(4×45)+45

p=225

Total number of people=225

This involves creating some equations.

First, these are what the letters I used stand for:

c = children

w = women

m = men

x = total population

Then, we must make an equation for each statement.

2/5x = m (2/5 of the people are men)

3c = w (there are 3 times as many women than children)

45+c = m (there are 45 more men than children)

Now, let's start plugging in our numbers:

x = all the men, women, and children

2/5(m+w+c) = m

2/5 (45+c +3c + c) = m     [Now simplify]

2/5 (45 + 5x) = m       [Now Distribute]

2/5(45) + (2/5)(5x) = m

2c + 18 = m    [Above we stated that there were the same amount as men as c +45]

2c + 18 = 45 +c     [Now set equal to c]

2c (-c) +18 = 45 +c (-c)

c+18 (-18) = 45 (-18)

c = 27

Now that we know that there was 27 children, we can plug 27 in for c in the other equations.

MEN = 27 + 45

WOMEN = 3(27)

CHILDREN = 27

Now add those three answers to find your total!

the correct answer is 45x

9×5=45 then add the x