The sum of two numbers is 15 .If the sum their reciprocal is 3/10 ,find the number​

Question

The sum of two numbers is 15 .If the sum their reciprocal is 3/10 ,find the number​

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Evelyn 3 weeks 2021-09-10T00:51:14+00:00 2 Answers 0 views 0

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    0
    2021-09-10T00:52:17+00:00

    Answer:

    Let the 1st natural number be x. And the 2nd natural number is (15 – x). Hence, the numbers are 10 and 5 or 5 and 10.

    0
    2021-09-10T00:53:08+00:00

     \huge \sf \color{purple}{\underline{\underline{Answer}}} :

    Two numbers are 5 and 10

     \huge \sf \color{purple}{\underline{\underline{Solution}}}:

    ✯ Let the number be x .

    ✯ Then the other number is 15 – x.

     \sf \color{brown}{Using \: the \: given \: information \: , we\: get }

      \sf \frac{1}{x}+\frac{1}{15-x}=\frac{3}{10} \\ \\ \sf \frac{15-x+x}{x(15-x)}=\frac{3}{10} \\ \\ \sf \frac{15}{(15x-x²)}=\frac{3}{10} \\ \\ \sf 150=45x-3x² \\ \\ \sf 3(x²-15+50)=0 \\\\ \sf x²-15+50=0 \\ \\ \sf x²-5x-10x+50 =0 \\ \\ \sf (x-10)(x-5)=0 \\ \\ \sf x-10=0 \: \: \ \ \ OR \ \ \ \ \sf x-5 \\ \\ \sf\boxed{ \colorbox{lightgreen}{x=10}} \ \ \ \ or \ \ \ \ \boxed{\colorbox{lightgreen}{ x = 5 }}

    When x = 10 , then the other number is 15-5 = 10

    When x = 5, then the other number is 15-5 = 10

     \color{red}━━━━━━━━━━━━━━━━━━

    \sf \color{blue}{Hence, \ the \ two \ numbers \ are \ 5 \ and \ 10  }

     \color{red}━━━━━━━━━━━━━━━━━━

     \color{red}━━━━━━━━━━━━━━━━━━

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