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a certain number decreased by 4 is equal to 8 increased by the quotient of the same number and 5. what is the number?

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  • JasonM
    Lv 7
    1 decade ago
    Favorite Answer

    Let x be the number.

    Then x - 4 = 8 + x/5

    If x = 15, then we have 15 - 4 = 8 + 3, which is true since both sides would equal 11.

    So, x =15 is such a number.

  • 1 decade ago

    the number is 15. 15-4 = 11 15/5= 3+8=11

  • 1 decade ago

    Call this certain number 'n' (I would think it would be better to call it an 'uncertain' number at this moment).

    The certain number decreased by four: n - 4,

    The quotient of the certain number and five: n ÷ 5,

    Eight increased by that quotient: 8 + n/5.

    Set these equal:

    n - 4 = 8 + n/5

    is your equation to solve.

    n - 4 = 8 + n/5,

    multiply both sides by 5:

    5n - 20 = 40 + n,

    add 20 to both sides:

    5n =60 + n,

    subtract 'n' from both sides:

    4n = 60,

    divide both sides by 4:

    n = 15

    voilà!

  • 1 decade ago

    let x equal the number

    certain number decreased by 4 is the same as x-4

    8 increased by the quotient of the same number and 5 is the same as 8+(x/5)

    set the two equations equal.... x-4=8+(x/5)

    get both x's on the right side by subtracting...

    -4=8+(x/5)-x

    subtract 8 from the right side...

    -12=(x/5)-x

    now to subtract, find the common denominator (5) for (x/5)-x...

    -12=(x/5)-(5x/5)

    multiply by 5 on both sides to eliminate the fraction...

    -60=x-5x

    subtract the like terms...

    -60=-4x

    finally, divide to get x alone...

    x=15

    another way, if you have a graphing calculator, is to put each side of the equation into Y= (put the left side in Y1 and the right in Y2) and graph. then, you can find the intersection, and the x-coordinate will be your final answer!

    thanks for distracting me from my own math homework...

    Source(s): me and math experiance
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  • 1 decade ago

    Make an equation based on the word problem (and always remember to look for negative answers, although in this case there are none).

    The equation is as follows:

    x - 4 = 8 + x/5

    First add 4 to both sides yielding

    x = 12 + x/5

    Second, subtract x/5 from both sides to get your variable on one side of the equation:

    x - x/5 = 12

    Remember that x and 5x/5 are equivalent. Understanding this will make the next step easier

    5x/5 - x/5 = (5x - x)/5 = 4x/5 = 12

    Now multiply both sides by 5

    4x = 60

    then divide by 4

    x = 15

    And there you have it.

  • 1 decade ago

    x-4=8+(x/5)

    15-4=11

    8+3=11

    My answer would be 11

  • 1 decade ago

    3?

  • 1 decade ago

    Your math teachers phone #

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