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?

Accepted Solution

Answer:Total number of people=225Step-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 1Total number of women (w)=3×total number of children (c)w=3 c...equation 2Total number of men (m)=Total number of children (c)+45m=c+45...equation 3The total number of people (p)=Number of women (w)+number of children (c)+number of men (m)where;Number of women (w)=3 cNumber of children (c)=cNumber of men (m)=c+45replacing;The total number of people (p)=3 c+c+(c+45)p=4 c+45The total number of people can be expressed as;p=4 c+45since the total number of men (m)=(2/5)pm=2/5(4 c+45)=(8/5) c+18....equation 4Equating equation 4 to equation equation 3(8/5) c+18=c+45(8/5) c-c=45-18(3/5) c=27c=27×5/3c=45Total number of people, p=4 c+45replacing with c=45p=(4×45)+45p=225Total number of people=225