several friends each had 2/5 of peanuts left over from the baseball game.they realized that they could have bought 2 fewer bags of peanuts between them .how many friends went to the game?

Drawing a picture would help.

it’s 5

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To solve this problem, we need to set up an equation based on the given information.

Let's assume there were 'x' friends who went to the game.

Each friend had 2/5 of the peanuts left over, so together they had 2/5 * x bags of peanuts left over.

The problem states that if they had bought 2 fewer bags of peanuts, they would have had the same amount as they ended up with. In other words, the number of bags they had is equal to the number of bags they should have bought minus 2.

So, setting up the equation:

2/5 * x = (x/5) * (2x/5) - 2

Simplifying this equation will help us solve for 'x'.

Multiplying both sides by 5 to remove the fraction:

2x = 2x^2/5 - 10

Multiplying both sides by 5 to remove the denominator:

10x = 2x^2 - 50

Rearranging to set it equal to zero:

2x^2 - 10x - 50 = 0

Now, we can solve this quadratic equation to find the value of 'x':

Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)

The coefficients for our equation are: a = 2, b = -10, c = -50

Substituting these values into the quadratic formula:

x = (-(-10) ± √((-10)^2 - 4*2*(-50))) / (2*2)
x = (10 ± √(100 + 400)) / 4
x = (10 ± √500) / 4

Now, simplify further:

x = (10 ± 10√5) / 4
x = (5 ± 5√5) / 2

So, there are two possible solutions for 'x':

1. x = (5 + 5√5) / 2 ≈ 8.045
2. x = (5 - 5√5) / 2 ≈ 0.955

Since the number of friends cannot be a decimal, we can conclude that there were approximately 8 friends who went to the game.