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2 December, 09:20

This year, the Start-of-Term feast had three desserts: chocolate eclairs, raspberry tarts, and jam doughnuts. On the dessert table, there were two doughnuts for every three eclairs, and six eclairs for every five tarts. How many tarts were on the dessert table if there were a total of 1320 desserts?

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  1. 2 December, 12:17
    0
    Each unit of dessert consists of five tarts, six eclairs and four doughnuts (since there are two for every three eclairs, or four for six). Each unit is therefore 15 deserts. 1320 deserts is 88 units. Each unit has five tarts, so the number of tarts is 88 times 5, or 440.
  2. 2 December, 12:48
    0
    Let

    x = chocolate eclairs

    y = raspberry tarts

    z = jam donuts

    We write the following system of equations:

    z = (2/3) x

    x = (6/5) y

    x + y + z = 1320

    Solving for y:

    z = (2/3) (6/5) y

    z = (4/5) y

    then

    (6/5) y + y + (4/5) y = 1320

    3y = 1320

    y = 1230/3 = 410

    answer

    there were 410 tarts on the dessert table
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