Question

The sum of two numbers is 38. The greater number is 8 more than the other number. Find each number. Use a system of linear equations to justify your answer.

Answer 1

Let one number be x and another be y

The sum of two numbers is 38

x + y = 38

x = 38 - y

The greater number is 8 more than the other number.

x - y = 8

x = 8 + y

solve both equations:

8 + y = 38 - y

y + y = 38 - 8

2y = 30

`{{\bold{{{{{ \green{y = 15}}}}}}}}`

solve for x:

x = 8 + y

x = 8 + 15

`{{\bold{{{{{ \green{x = 23}}}}}}}}`

`{{\bold{{{{{ \red{so, x \: = 23 \: and \: y \: = 15}}}}}}}}`

Answer 2

x = 23 and y = 15

Let one number be x and another be y

The sum of two numbers is 38

x + y = 38

x = 38 - y

The greater number is 8 more than the other number.

x - y = 8

x = 8 + y

solve both equations:

8 + y = 38 - y

y + y = 38 - 8

2y = 30

y = 15

solve for x:

x = 8 + y

x = 8 + 15

x = 23