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Two pieces of cake weigh as much as one apple and one cherry. One apple weighs as much as five cherries and one piece of cake. How many cherries weigh as much as one apple?

  • Math -

    first let's represent their weights using variables:
    let C = weight of one piece of cake
    let A = weight of one apple
    let H = weight of one cherry
    from the first statement,
    (1) 2C = A + H
    for the second statement,
    (2) A = 5H + C
    now we need to find how mach does cherries weigh as much as 1 apple. thus we need to manipulate these equations so that the weight of cake, C will not be involved in the final equation (in other words, we'll eliminate C)
    first, from equation (2), we transpose C to the left side and A to the right side, and multiply both sides by 2, and it becomes:
    -2C = -2A + 10H
    then we add this to equation (1):
    2C = A + H
    -2C = -2A + 10H
    0 = -A + 11H
    A = 11H
    therefore, 1 apple weighs as much as 11 cherries.

    hope this helps~ :)

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