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?
Use simple working please
There are M males, F females, b boys, g girls
M = 3F
5/6 M = b
2/3 F = g
b = g + 121
make some substitutions to get
5/6 M = g+121
5/6 (3F) = g+121
5/6 (3F) = 2/3 F + 121
5/2 F = 2/3 F + 121
11/6 F = 121
11F = 726
F = 66
So, working back through the substitutions,
M = 3F = 198
M+F = 264 <-- no. of people
check:
5/6 of 198 = 165 boys, so 33 men
2/3 of 66 = 44 girls, so 22 women
165=44+121 so the boy/girl difference works too.
men+women = 33+22 = 55 adults