The denominator of a rational number is greator thqn its numerator by 7. If the numerator is increased by 17 and the denominator is decrease

Question

The denominator of a rational number is greator thqn its numerator by 7. If the numerator is increased by 17 and the denominator is decreased by 6 the new number becomes 2. Find the original number

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Isabelle 12 hours 2021-10-13T06:29:09+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-13T06:30:11+00:00

    AnSwer:

    The original number is 15/22.

    ExPlanation:

    Let numerator be x.

    So, the denominator will be x+7.

    According to the question,

    • If numerator is increased by 17 = x+17

    • When denominator is decreased by 6=x+7-6=x+1.

    Then the above value must be equal to 2.

    So,

     : \implies \sf \:  \:  \:  \dfrac{x + 17}{x + 1} = 2 \\  \\ : \implies \sf \:  \:  \:x  + 17 = 2(x + 1) \\  \\ : \implies \sf \:  \:  \:x + 17 = 2x + 2 \\  \\ : \implies \sf \:  \:  \:17 - 2 = 2x - x \\  \\ : \implies \sf \:  \:  \:{ \underline{ \boxed{ \sf{ \pink{x = 15}}}}}  \: \bigstar

    So ,the value of numerator will be x= 15.

    Now as per given conditions,

    • Denominator is greater than its numerator by 7.

    So,

      \bigstar \:  \sf \: Denominator \: : -  \\  \\  \implies \sf \: x + 7 \\  \\ \implies \sf \:15 + 7 \\  \\ \implies \sf \:{ \underline{ \boxed{ \sf{ \purple{22}}}}}  \: \bigstar

    So, the fraction is \sf\dfrac{15}{22}

    Original no. is fraction which is \sf\dfrac{15}{22}

    0
    2021-10-13T06:30:20+00:00

    \sf{\underline{\huge{\boxed{\purple{\mathfrak{Question}}}}}}

    • The denominator of a rational number is greator thqn its numerator by 7. If the numerator is increased by 17 and the denominator is decreased by 6 the new number becomes 2. Find the original number

    \\ \sf{\underline{\huge{\boxed{\purple{\mathfrak{Solution}}}}}}

    ✏ let the numerator be x

    ✏ therefore denominator = x + 7

    Given :

    ✏ numerator increased by 17 = x + 17

    ✏ denominator decreased by 6 = x + 7 – 6

    denominator = x + 1

    \sf\dfrac{numerator}{denominator} = 2

    Explanation :

    \sf\dfrac{x + 17 }{ x + 1 } = 2

    • cross multiplication

    \sf x + 17 = 2x + 2

    \sf 17 - 2 = 2x - x

    \sf x = 15

    \\ \sf{\bold{\green{\underline{\underline{numerator \: = \: 15 }}}}}

    \sf denominator \: = x + 7

    \sf denominator \: = 15 + 7

    \sf denominator \: = 22

    \\ \sf{\bold{\green{\underline{\underline{denominator  \: = \: 22 }}}}}

    \\\sf{\underline{\boxed{\purple{\mathfrak{Required\: fraction\: = \dfrac{15}{22}}}}}}

    _________________❤

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