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

since both sides equal, there are infinitely many olutions.