The sum of two numbers is 56. Seven times the smaller number is 12 more than three times the larger number. Find the numbers.

x = 18

y = 38

Step-by-step explanation:

Let the smaller number be = x

Let the larger number be = y

Sum of the number, x + y = 56 ( 1 )

Seven  times smaller number = 7x

Three times larger number = 3y

Seven times smaller = 12 more than 3times larger , 7x = 12 + 3y ( 2 )

Solve ( 1 ) and ( 2 )

x + y = 56  => x = 56 - y

Substitute x in ( 2 )

7x - 3y = 12

7(56 - y) - 3y = 12

392 - 7y - 3y = 12

-10y =  12 - 392

-10y = - 380

y = 38

Substitute y in ( 1 )

x + y = 56

x + 38 = 56

x = 56 - 38

x = 18