Question

The sum of two numbers is 8, and one of them with 22 added to it is five times the other number​

Answer 1

Given:

Sum of two numbers is 8

Sum of two numbers is 8

22+one number= 5 times the other number

To find:

The numbers

Explanation:

Let the numbers be x and y

According to the given information,

$x + y = 8.....(1)$

$x + 22 = 5y........(2)$

$\sf from \: (1) we \: can \: write \: y=(8-x)$

substituting the value in the equation (2)

$= > x + 22 = 5(8 - x) \\ \\ = > x + 22 = 40 - 5x$

$= > x + 5x = 40 - 22 \\ \\ = > 6x = 18 \\ \\ = > \boxed{ \sf \: x = 3}$

substituting value of x in equation (1)

$= > 3 + y = 8 \\ \\ = > \boxed{ \sf \: y = 5}$

Therefore the numbers are 3,5

Answer 2

Let ,

The two numbers be x and y

By the given condition ,

$\star$x + y = 8 ------------ eq (i)

$\star$x + 22 = 5y ------------ eq (ii)

Using elimination method , subtract eq (ii) from eq (i)

$\sf \implies (x - 5y) - (x + y) = - 22 - 8 \\ \\ \sf \implies</p><p>- 6y = - 30 \\ \\ \sf \implies </p><p>y = 5$

Put the value of y = 5 in equation (i)

$\sf \implies x + 5 = 8 \\ \\ \sf \implies</p><p>x = 8 - 5 \\ \\ \sf \implies </p><p>x = 3$

Hence , the required numbers are 5 and 3