Tierra, Nico, and Alex had $865 altogether. Tierra spent 2/5 of her money. Nico spent $40 , and Alex spent twice as much as Tierra. If the three friends had the same amount of money left, how much money did Alex have in the beginning.

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Let's solve this step by step.

Step 1: Find the total amount of money spent.
Since Tierra spent 2/5 of her money, she had 3/5 left.
Nico spent $40, and Alex spent twice as much as Tierra.

Tierra's money left = 3/5
Nico's money left = (total - 40)
Alex's money left = 2 * Tierra's money left

Step 2: Set up an equation using the given information.
Let's say Tierra had x dollars in the beginning.
According to the given information, we have:

Tierra's money left = 3/5 * x
Nico's money left = total - 40
Alex's money left = 2 * (3/5 * x)

Step 3: Find the total amount of money they had.
Since they all had the same amount of money left, we can set the equations equal to each other:

3/5 * x + total - 40 = 2 * (3/5 * x)

Step 4: Solve the equation for x.
Let's solve the equation:

3/5 * x + total - 40 = 6/5 * x

Multiply both sides by 5 to eliminate the fractions:

3x + 5(total) - 200 = 6x

Combine like terms:

5(total) - 200 = 6x - 3x
5(total) - 200 = 3x

Move all the terms containing x to one side and the constant terms to the other side:

3x - 5(total) = -200

Step 5: Calculate the value of x.
Let's solve the equation:

3x - 5(total) = -200

First, let's isolate x by adding 5(total) to both sides:

3x = 5(total) - 200

Next, divide both sides by 3:

x = (5(total) - 200) / 3

Step 6: Calculate the value of x using the given information.
We know that Tierra, Nico, and Alex had $865 altogether.

So, the equation becomes:

x = (5(865) - 200) / 3

Simplifying:

x = (4325 - 200) / 3
x = 4125 / 3
x ≈ 1375

Therefore, Alex had approximately $1375 in the beginning.

To solve this problem, let's start by representing the information given in the question using variables.

Let:
- The amount of money Tierra had initially be represented by T.
- The amount of money Nico had initially be represented by N.
- The amount of money Alex had initially be represented by A.

We are given the following equations:
1) T + N + A = $865 (Since they had $865 altogether)
2) Tierra spent 2/5 of her money.
3) Nico spent $40.
4) Alex spent twice as much as Tierra.

From equation 2, we can conclude that Tierra has (1 - 2/5) = 3/5 of her money left.

From equation 4, we can conclude that Alex has 2 times the money Tierra has left.

Since the three friends had the same amount of money left, we can write the following equation:
3/5 * T = N - $40 = A - $((3/5)T + 2) * 2

Simplifying equation 3/5 * T = N - $40, we get:
3T = 5N - $200 -----(5)

Simplifying equation N - $40 = A - $((3/5)T + 2) * 2, we get:
5N - $200 = A - $((3/5)T + 2) * 2 -----(6)

Substituting equation (5) into equation (6), we get:
5T = A - $((3/5)T + 2) * 2 -> 5T = A - $((3/5)T + 2) * 2
-> 5T = A - (3T/5 + 2) * 2
-> 5T = A - (6T/5 + 4)
-> 5T = A - (6T + 20)/5
-> 25T = 5A - (6T + 20)
-> 31T - 5A = -20

From equation 1, we know that T + N + A = $865, so we can substitute T = $865 - N - A into equation 31T - 5A = -20.

Substituting, we get:
31($865 - N - A) - 5A = -20
26615 - 31N - 31A - 5A = -20
26615 - 31N - 5A - 31A = -20
26615 - 36N - 36A = -20

Re-arranging this equation:
36N + 36A = 26635

At this point, we need to find values for N and A that satisfy this equation. Since there are multiple solutions, we can't determine the exact value for A without more information.