several friends each had 2/3 of a bag of peanuts left over from the basketball game. they realized that they could have bought 2 fewer bags of peanuts between them. how many friends went to the game?
2/(2/3) = 3
So, 3 people, each with 2/3 extra bag makes 2 extra bags.
Go eat some balls
To find out how many friends went to the game, let's work through the problem step by step.
Let's assume the total number of friends is represented by 'x'.
Each friend had 2/3 of a bag of peanuts left after the game. So, the total amount of peanuts left over is given by:
Amount of peanuts left = (2/3) * x
Now, the problem states that they could have bought 2 fewer bags of peanuts if they had shared from the beginning. So, the total number of peanut bags they could have bought is given by:
Total number of bags they could have bought = x - 2
Since each bag contains 1, the total number of peanuts they could have bought is:
Total number of peanuts they could have bought = (1) * (x - 2)
According to the problem, the amount of peanuts left over and the amount they could have bought is the same:
(2/3) * x = (1) * (x - 2)
To solve this equation, we can multiply both sides by 3 to eliminate the fraction:
2x = 3(x - 2)
Next, distribute the 3 to the terms inside the parentheses:
2x = 3x - 6
Now, we can subtract 3x from both sides:
2x - 3x = -6
Simplifying further:
-x = -6
To isolate x, we can multiply both sides by -1 which flips the sign:
x = 6
Therefore, there were 6 friends who went to the game.