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the ratio of Simone's pocket money to Fiona's pocket money was 2:3. After Fiona had received $5 from her mother, the ratio of Simone's pocket money to Fiona's pocket money became 4:7. how much pocket money did both of them have at first?

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2 answers
  1. s = 2 f/3

    s = 4 (f+5) /7

    --------------------
    2 f/3 = 4 f/7 + 20/7

    2*21 f/3 = 4*21 f/7 + 20*21 /7

    14 f = 12 f + 60

    2 f = 60
    so
    f = 30
    s = 2 f/3 = 20
    =======================
    check
    s/f = 20/30 = 2/3 yes

    s/(f+5) = 20/35 = 4/7 yes, it worked

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  2. how about this approach:

    Simone's money --- 2x
    Fiona's money --- 3x

    after mom's gift:
    2x/(3x+5) = 4/7
    14x = 12x + 20
    2x = 20
    x = 10

    so Simone had 2x or $20
    Fiona had 3x or $30

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