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+18 ... equation 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