During a dull football game,1/4 spectators were left after 1 hour.During the next hour 20,000 spectators left. there were 1/12 of the original number of spectators still watching the game. how many spectators were originally present.
x of them were there
x/4 after an hour
x/4 - 20,000 after two hours
that is x/12
so
x/12 = x/4 - 20,000
3 x/12 - x/12 = 20,000
x/6 = 20,000
x = 120,000 big game
Let's assume the original number of spectators present at the football game is "x".
After 1 hour, 1/4 of the spectators are left, which means there are (3/4)x spectators remaining.
During the next hour, 20,000 spectators left, so the number of spectators remaining is (3/4)x - 20,000.
According to the given information, there were 1/12 of the original number of spectators still watching the game, which means (1/12)x spectators remaining.
Setting up an equation based on this information, we can say:
(3/4)x - 20,000 = (1/12)x
To solve this equation, we will multiply both sides by 12:
12 * (3/4)x - 12 * 20,000 = 12 * (1/12)x
9x - 240,000 = x
Subtracting x from both sides:
9x - x = 240,000
Combining like terms:
8x = 240,000
Dividing both sides by 8:
x = 240,000 / 8
Simplifying:
x = 30,000
Therefore, the original number of spectators present at the football game was 30,000.
To solve this problem, let's break it down step by step.
Let's assume the original number of spectators as 'x.'
After the first hour, 1/4 of the spectators were left. So, the number of spectators remaining after the first hour would be (1 - 1/4)x.
In the next hour, 20,000 spectators left. So, the number of spectators remaining after the second hour would be ((1 - 1/4)x) - 20,000.
According to the problem, 1/12 of the original number of spectators were still watching the game. So, we can set up the equation:
((1 - 1/4)x) - 20,000 = 1/12 of x
To solve this equation, we can simplify it:
(3/4)x - 20,000 = 1/12 of x
Now, let's get rid of fractions by multiplying both sides of the equation by the least common multiple (LCM) of the denominators, which is 12:
12 * (3/4)x - 12 * 20,000 = 12 * (1/12)x
9x - 240,000 = x
Next, let's move all the x terms to one side of the equation:
9x - x = 240,000
8x = 240,000
To isolate x, we divide both sides of the equation by 8:
x = 240,000 / 8
x = 30,000
Therefore, there were originally 30,000 spectators present at the football game.