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 ?
Accepted Solution
A:
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