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July 28, 2014

July 28, 2014

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

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