Question

The sum of two numbers is 15 if the sum of their reciprocal is 3 by 10 find the numbers

Answer 1

Answer:

A = 5 and B = 10

Step-by-step explanation:

let the two numbers be A and B

=>A+B=15                      .............(1)

and

1/A +1/B=3/10

⇒(A+B)/AB = 3/10

from (1)

(A+B)/AB = 15/AB

⇒15/AB = 3/10

⇒AB = 50        ............(2)

solving (1) and (2)

A = 10 and B = 5

or

A = 5 and B = 10

Answer 2

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

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.

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

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

$\color{red}━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━$

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

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

$\color{red}━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━$

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

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