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    Systems of Equations : Five Word Problems

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    There are hens + rabbits. The heads = 50 the feet = 134. How many hens & how many rabbits ?
    Flies + spiders sum 42 heads and 276 feet. How many of each class?
    J received $1000 and bought 9 packs of whole milk & skim milk that totalled $960 - How many packs bought of each kind?
    A number is composed of two integers and its sum is 9 if the order is inverted the result is equal to the given number plus 9 more units - find the number.
    Determine 2 numbers such that the difference of its squares is 120 and the sum is 6.
    If I have 30 coins of two kinds 5 cents and 1 cent can I have a total of 78?
    A rectangle has a perimeter of 392 m calculate its dimensions if the length is 52 m longer than the width.

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    Solution Preview

    1.)
    Let there are x hens (2 feet) and y rabbits (4 feet).
    Heads,
    x+y = 50 ....(1)
    Feets,
    2x + 4y = 134
    => x + 2y = 67 ..(2)
    Eqn. (2) - (1), we get,
    y = 17
    thereforem from Eqn. (1), x = 50 - 17 = 33
    Hence, hens = 33 and rabbits = 17 --Answer

    2.)
    Let there are x flies and y spiders. Flies have 6 feets and spiders have 8 feets.
    Heads,
    x+y = 42 ..(1)
    Feets,
    6x+8y = 276
    => 3x+4y = 138 ...(2)
    Eqn. (1)*3:
    3x + 3y = 126 ....(1)*3
    Eqn. (2) - (1)*3, we get,
    y = 12
    Therefore, from Eqn. (1) eliminate y, ...

    Solution Summary

    Five word problems are solved using systems of equations. The expert calculates the dimensions of lengths and widths.

    $2.19

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