Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6.

Discussion in 'Calculator Requests' started by math_celebrity, Feb 19, 2017.

  1. math_celebrity

    math_celebrity Administrator Staff Member

    Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6. When you divide x by 11 you get the same quotient but a remainder of 2. Find x.

    Use the quotient remainder theorem
    A = B * Q + R where 0 ≤ R < B where R is the remainder when you divide A by B

    Plugging in our numbers for Equation 1 we have:
    • A = x
    • B = 7
    • Q = q
    • R = 6
    • x = 7 * q + 6
    Plugging in our numbers for Equation 2 we have:
    • A = x
    • B = 11
    • Q = q
    • R = 2
    • x = 11 * q + 2
    Set both x values equal to each other:
    7q + 6 = 11q + 2

    Using our equation calculator, we get:
    q = 1

    Plug q = 1 into the first quotient remainder theorem equation, and we get:
    x = 7(1) + 6
    x = 7 + 6
    x = 13

    Plug q = 1 into the second quotient remainder theorem equation, and we get:
    x = 11(1) + 2
    x = 11 + 2
    x = 13
     

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