Question

The sum of two numbers is 18.The sum of their reciprocal is 1/4.Find the numbers.

Answer 1

Solution is attached below

Answer 2

Answer:

x = 6, y=12 or x = 12 ,y=6

Step-by-step explanation:

Let the numbers be x and y

We are given that the sum of two numbers is 18

So, $x+y=18$---1

We are also given that the sum of their reciprocal is 1/4.

So, $\frac{1}{x}+\frac{1}{18-x}=\frac{1}{4}$

Substitute the value of y from 1

$\frac{18-x+x}{x(18-x)}=\frac{1}{4}$

$\frac{18}{x(18-x)}=\frac{1}{4}$

$\frac{18 \times 4}{x(18-x)}=1$

$\frac{72}{18x-x^2}=1$

[tex]72=18x-x^2[tex]

[tex]x^2-18x +72=0[tex]

[tex]x^2-12x-6x +72=0[tex]

[tex]x(x-12)-6(x -12)=0[tex]

[tex](x-6)(x-12)=0[tex]

[tex]x=6,12[tex]

when x is 6

y = 18-x=18-6=12

when x is 12

y = 18-x=18-12=6

So, x = 6, y=12 or x = 12 ,y=6