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Please show the quickest way to do this question?

Amanda has 20 coins in her purse. She has only 10c,20c and 50c coins, and their total value is $5. If she has more 50c than 10c coins, how many 10c has she?

Thank You

  • MATHS -

    Are you in algebra using variables 'c'?

  • MATHS -

    I'm not sure what you mean.

  • MATHS -

    What grade are you in?

  • MATHS -

    YEAR 4

  • MATHS -

    c stands for cents?

  • MATHS -

    yes c stands for cents.

  • MATHS -

    I got 4 x 50c = $2

    2 x 10c = 20 c

    14 x 20c = $2.80c

    so she has 2 x 10c

  • MATHS -

    Since you are in year 4, you will be able to solve this algebraically.
    let the number of 10c pieces be x
    let the number of 20c pieces be y
    let the number of 50c pieces be (20-x-y)

    10x + 20y + 50(20-x-y) = 500
    reduces to
    4x + 3y = 50
    so we need positive integer solutions for x and y
    clearly x has to be between 0 and 13
    after only two tries, I got
    x = 2, and y = 14
    then
    number of 10c pieces = 2
    number of 20c pieces = 14
    number of 50c pieces = 20-2-14 = 4

    check: 2x10 + 14x20 + 4x50 = 500

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