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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To solve this problem, we'll break it down step by step:
Let's start by setting up equations for each person's spending:
Tierra spent 2/5 of her money. Let's say Tierra had x dollars in the beginning.
The amount Tierra spent is 2/5 * x.
Nico spent $40.
So, the amount Nico spent is $40.
Alex spent twice as much as Tierra.
So, the amount Alex spent is 2 * (2/5 * x) = 4/5 * x.
Now, let's set up an equation for the total amount spent:
Tierra's spending + Nico's spending + Alex's spending = Total spending
(2/5 * x) + $40 + (4/5 * x) = Total spending
We know that the three of them had the same amount of money left.
So, Tierra, Nico, and Alex had equal amounts of money left.
Since they had equal amounts of money left, the equation becomes:
Total money in the beginning - Total spending = Total money left
x + x + x = $865 - [(2/5 * x) + $40 + (4/5 * x)]
Now, let's solve the equation:
3x = $865 - [(2/5 * x) + $40 + (4/5 * x)]
Simplifying the right side:
3x = $865 - (6/5 * x + $40)
3x = $865 - (6/5 * x) - $40
3x = $865 - $40 - (6/5 * x)
3x = $825 - (6/5 * x)
To get rid of the fraction, let's multiply the equation by 5 to clear the denominator:
15x = 5 * $825 - 5 * (6/5 * x)
15x = $4125 - 6x
Next, combine like terms:
15x + 6x = $4125
21x = $4125
Now divide both sides by 21 to solve for x:
x = $4125 / 21
Calculating x yields:
x ≈ $196.43
Therefore, Tierra had approximately $196.43 in the beginning.
Since Alex spent twice as much as Tierra, we can calculate how much Alex had in the beginning:
Alex had 2 * $196.43 = $392.86
So, Alex had approximately $392.86 in the beginning.