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17 September, 15:47

a weight lifter uses both 2 kg blocks as well as 5 kg blocks to set up his bar. he has a total of 30 blocks if the total weight of the bar is observed to be 120 kg then calculate the number of 5 kg blocks and 2 kg blocks

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  1. 17 September, 16:07
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    The number of the 2 kg blocks is 10

    The number of the 5 kg blocks is 20

    Step-by-step explanation:

    Let the number of the 2 kg blocks be x and the number of the 5 kg blocks be y.

    The total number of blocks in terms of x and y is;

    x + y

    We are informed that he has a total of 30 blocks, implying that;

    x + y = 30

    The total weight of the bar in terms of x and y will be;

    2x + 5y

    We are also informed that the total weight of the bar is observed to be 120, implying that;

    2x + 5y = 120

    We therefore have two equations in two unknowns.;

    x + y = 30

    2x + 5y = 120

    We can solve these equations simultaneously via elimination method;

    multiply the first equation by 2;

    2x + 2y = 60

    2x + 5y = 120

    Subtracting the first equation from the second one yields;

    5y - 2y = 120 - 60

    3y = 60

    y = 20

    But x + y = 30, implying that;

    x = 30 - 20

    x = 10
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