Question

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

Answer 1

Answer:

X + Y  = 15

1/X + 1/Y = 3/10

I/X + 1/(15-X) = 3/10

(15-X)+X/(X(15-X)) = 3/10

150 = 3(15X-X**2)

3X**2 - 45X + 150 = 0

X**2 -15X + 50 = 0

X**2 - 10X - 5X + 50 = 0

X(X-10) - 5(X-10) =0

(X-5)(X-10)=0

X = 5

Y = 15-X = 15-5 = 10  

Step-by-step explanation:

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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