at a baseball game, there were three times as many males as females. 5/6 of the males were boys and the rest were men. 2/3 of the females were girls and the rest were women. Given that there were 121 more boys than girls, how many adults were there at the baseball game?
number of girls --- x
number of boys --- x+121
number of females -- y
number of males ---- 3y
number of women = y - x
number of men = 3y - x - 121
"5/6 of the males were boys " ---> (5/6)(3y) = x + 121
15y = 6x + 726
6x - 15y = -726
2x - 5y = -242 ---- A
"2/3 of the females were girls " --- (2/3)y = x
2y = 3x
y = 3x/2 sub this into A
2x- 5(3x/2) = -242
4x - 15x = -484
-11x = -484
x = 44
then y = 3(44)/2 = 66
so we have:
44 girls and 165 boys
66 females and 198 males
of which 22 are adult women and 33 are adult men
for a total of 55 adults at the game
check:
5/6 of males = (5/6)(198) = 165 , which is the number of boys
2/3 of females = (2/3)(66) = 44, which is the number of girls
All checks out