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 had the same amount of money left, how much money did alex have in the begging?
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Let's solve this step by step:
Let's assume that Alex had initially x dollars.
- Tierra spent 2/5 of her money, so she had 3/5 remaining.
- Nico spent $40, so he had (x - $40) remaining.
- Alex spent twice as much as Tierra, so he spent 2 * (3/5) * x = 6/5 * x.
Since they all had the same amount of money left, we can set up an equation:
3/5 * x = (x - $40) = 6/5 * x
To solve this equation, we need to find a common denominator:
Multiply both sides by 5 to get:
3x = 5(x - $40) = 6x
Next, simplify:
3x = 5x - $200 = 6x
Subtract 5x from both sides:
3x - 5x = - $200
Combine like terms:
-2x = - $200
Divide both sides by -2:
x = - $200 / -2
Simplifying further:
x = $100
Therefore, Alex had $100 in the beginning.