Find the number of pairs of two numbers whose HCF is 5 and their sum is 50. kindly help!?

5 Answers

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  • 7 months ago

    x + y = 50

    HCF = 5

    5, 45: 15, 35; [35, 15; 45, 5]

  • Ian H
    Lv 7
    7 months ago

    At first we might think of this list

    5, 45

    10, 40

    15, 35

    20, 30

    25, 25

    But 10 rather than 5 is the HCF with

    10, 40 and

    20, 30

    and 25, 25 obviously has an HCF of 25,

    so that just leaves 5, 45 and 15, 35

  • Amy
    Lv 7
    7 months ago

    Both numbers are multiples of 5, so let's call them 5x and 5y.

    The constraint is that x and y are positive integers and are relatively prime to each other.

    5x + 5y = 50

    x + y = 10

    List all pairs (x,y) that sum to 10 and meet the stated constraint.

  • Dylan
    Lv 6
    7 months ago

    5a+5b=50

    a+b=10 with no common factors

    1 and 9

    3 and 7

    So....

    5 and 45

    15 and 35

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  • Pope
    Lv 7
    7 months ago

    It should take only a moment to check all non-negative integer pairs that are divisible by five and whose sum is 50. Let the first of the pair increase from zero to 25.

    0, 50 ... HCF = 50; reject

    5, 45 ... HCF = 5

    10, 40 ... HCF = 10; reject

    15, 35 ... HCF = 5

    20, 30 ... HCF = 10; reject

    25, 25 ... HCF = 25; reject

    I count two qualifiers.

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