math

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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?

  • math -

    It 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 -

    I 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 -

    julia, 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 -

    plain and simple it is $385 they each had $165 left over

  • math -

    it is $385 and they each had $165 left

  • math -

    Simon 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?

  • math -

    It is $385

  • Poop -

    Shshshnsushs

  • math -

    385

  • Math -

    Hmmmmm..................its 385!

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