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?
m = 3f
5m/6 = b
2/3 f = g
b = g+121
So, solve all that and you get m/6 + f/3 = 77
To solve this problem, we can break it down into smaller steps. Let's begin by assigning variables to the unknowns.
Let's say the number of females is "x" and the number of males is "3x" (since there are three times as many males as females).
We know that 5/6 of the males were boys and the rest were men. So, out of the 3x males, 5/6 * 3x were boys, which is (5/6) * 3x = 5/2x. The remaining males were men, which is 3x - (5/2x) = (6/2x - 5/2x) = 1/2x.
Next, we know that 2/3 of the females were girls, so (2/3) * x were girls and the remaining females were women, which is x - (2/3)*x = (3/3x - 2/3x) = 1/3x.
Now, we are given that there were 121 more boys than girls. We can set up an equation to represent this:
(5/2x) - (2/3)x = 121
To solve this equation, we can multiply both sides by 6x to get rid of the denominators:
6x * [(5/2x) - (2/3)x] = 6x * 121
(15 - 4)x^2 = 6x * 121
11x^2 = 6x * 121
11x^2 = 726x
Now we can divide both sides by x to simplify the equation:
11x = 726
Dividing both sides by 11, we find:
x = 66
Now that we know the value of x, we can substitute it back into our equations to find the number of males and females:
Number of females (x) = 66
Number of males (3x) = 3 * 66 = 198
Number of boys = (5/2)x = (5/2) * 66 = 165
Number of men = (1/2)x = (1/2) * 66 = 33
Number of girls = (2/3)x = (2/3) * 66 = 44
Number of women = (1/3)x = (1/3) * 66 = 22
Finally, to find the number of adults, we add the number of men and women together:
Number of adults = Number of men + Number of women = 33 + 22 = 55
Therefore, there were 55 adults at the baseball game.