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Posted by **julia** on Thursday, February 24, 2011 at 7:24am.

- math -
**MathMate**, Thursday, February 24, 2011 at 9:11amIt is a problem of linear equations in three unknowns, t, n, a representing the initial amount of each person.

Hints:

The sum is $865, so

x+y+z=865 ... (1)

Tierra spent 2/5 of her money, so she has 3t/5 left.

Nico spent $40, so he has n-40 left.

Alex spent twice that Tierra spent, so he has a-(3t-5) left.

Equate money left for each person:

3t/5 = n-40 ...(2)

n-40 = a-3t+5 ...(3)

Solve equations (1), (2) and (3) in three unknowns t,n and a to get a, the amount Alex initially had.

I do not get round numbers for results, for example, Tierra had initially 4125/17=$242.65 (approximately).

- math-Mathmate could you look at please -
**Helper**, Thursday, February 24, 2011 at 10:35amI was working on this at the same tiime as you, but I arrived at a different answer.

x = amt Tierra had

2x/5 = amt Tierra spent

3x/5 = amt Tierra had left

y = amt Alex had

4x/5 = amt Alex spent

y - 4x/5 = amt Alex had left

z = amt Nico had

$40 = amt Nico spent

z - 40 = amt Nico had left

Three equations

x + y + z = 865

3x/5 = z - 40

z - 40 = y - 4x/5

Solve these equations simultaneously,

x + y + z = 865

3x/5 - z = -40

z + 4x/5 - y = 40

x = 275 (Tierra had)

y = 385 (Alex had)

z = 205 (Nico had)

2x/5 = 110 = (Tierra spent)

4x/5 = 220 = (Alex spent)

40 = (Nico spent)

Each had $165 left

275 - 110 = 165 (Tierra left)

385 - 220 = 165 (Alex left)

205 - 40 = 165 (Nico left)

- math-correction -
**MathMate**, Thursday, February 24, 2011 at 11:30amjulia, please go with Helper's answer.

Thank you helper, I made a mistake with Alex's spending.

It should read:

Tierra spent 2/5 of her money, so she has 3t/5 left.

Nico spent $40, so he has n-40 left.

Alex spent twice that Tierra spent, so he has**a-2(2t/5)**left.

Equate money left for each person:

3t/5 = n-40 ...(2)

n-40 = a-**a-2(2t/5)**...(3) "

Which obviously should give the same answer as yours.

- math -
**Joe**, Monday, April 11, 2011 at 4:31pmplain and simple it is $385 they each had $165 left over

- math -
**Joe**, Monday, April 11, 2011 at 4:32pmit is $385 and they each had $165 left

- math -
**Anonymous**, Thursday, November 6, 2014 at 10:21pmSimon and Jimmy had 167 stamps altogether. Simon gave47of his stamps to Trina, and Jimmy gave 37 stamps to Trina. Simon and Jimmy had the same number of stamps left. How many stamps did Jimmy have in the beginning?

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