Question

at a shopping mall,4/9 of the shoppers were children and 5/7 of the adults were woman.They were 1/2 as many boys as men.They were 90 more girls than boys. (a) what fraction of the shoppers in the shopping mall were men ? (b) How many shoppers were in the shopping mall ?

Answer 1

Short Answer: 315 Total Shoppers: (10/63) Men
Step One
Let the children = C
Let the adults = A
Let the Men = M
Let the Women = W
Let the Boys = B
Let the Girls = G
Let the total number of shoppers = T

Find the Fraction of Children
4/9 T = C

Find the fraction of adults
T - 4/9 T = A
5/9 T = A

Find the Fraction of Women
5/7 A = W
(5/7) (5/9) T = W
(25/63) T = W

Find the Fraction of Men 
Note if 5/7 of the adults are women then 2/7 of the adults are men.
2/7 A = M
2/7 5/9 T = M
10/63 = M <<<<<<< Answer for fraction of Men

Find the fraction of Boys. The boys = 1/2 the Men
1/2 M = B  
(1/2)(2/7)(5/9)T = B
5/63 T = B

Find The fraction of Girls
(4/9)T - B  = G
4/9 T - 5/63 T = G
(28 / 63) T - (5/63/)T = G 
(28/63 - 5/63)T = G
(23 /63) T = G

Find the total number of shoppers.
B + 90 =  G
(5/63) T + 90 = (23/63) T 
90 = (23/63)T - (5/63)T
90 = (18/63)T 
90 (63/18) =T
T = 5*63
T = 315   Answer for total number of Shoppers

Note see above for the fraction of men.