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

Looking at all the "Related Questions" below, you must have a typo.

Most say "Alex spent twice as much as Terry"

let Terry's amount be x
let Nick's amount be y
let Alex' amount be 865-x-y

after the spending:
Terry has (3/5)x = 3x/5
Nick has y-40

Terry spend 2x/5
so Alex spent 4x/5
and Alex has left 865-x-y - 4x/5
= (4325-5x-5y - 4x)/5
= (4325 - 9x - 5y)/5

all have the same amount left over ...
3x/5 = y-40
3x= 5y - 200
3x - 5y = -200 , #1

(4325 - 9x - 5y)/5 = y-40
4325 - 9x - 5y = 5y - 200
9x + 10y = 4525 , #2

#1 times 2
6x - 10y = -400
9x - 10y = 4525
add them ...
15x = 4125
x = 275
then in #1:
3(275) - 5y = -200
y = 205

Terry had 275
Nick had 205
Alex had 865-275-200 = 385

check:
Terry has (3/5)275 or 165 left
Nick has 205-40 or 165 left
Terry spent (2/5)(275) or 110, so
Alex spent 220
leaving him with 385-220 = 165
ALL LOOKS GOOD

itz 2/5 for Teri so you didyour math wrong

Nevermind you're fine

To solve this problem, let's break it down step by step.

Step 1: Determine the amount of money Teri spent.
Given that Teri spent 2/5 of her money, we need to calculate 2/5 * Total amount. Let's represent this as 2/5 * T, where T is the total amount of money Teri had.

Step 2: Determine the amount of money Nick spent.
Given that Nick spent $40, we know that Nick had the same amount of money left as Teri after she spent her money. Therefore, Nick's starting amount was: T - (2/5 * T) = T(1 - 2/5) = T(3/5).

Step 3: Determine the amount of money Alex spent.
Given that Alex spent twice the amount Nick spent, we can calculate this as: 2 * (T(3/5)) = 2T(3/5) = 6T/5.

Step 4: Given that the remaining amount for each friend is the same, we can set up an equation:
(T - 2/5 * T) - $40 = (6T/5)

Step 5: Solve for T:
(3/5 * T) - $40 = (6T/5)
Multiply both sides by 5 to get rid of the denominators:
3T - 200 = 6T
Subtract 3T from both sides:
-200 = 3T
Divide both sides by 3:
T = -200/3
T ≈ -66.67

Step 6: Since money cannot be negative, we can conclude that there was an error or inconsistency in the given information. Please double-check the problem to ensure accuracy.