The sum of two numbers is 48. if the larger number is 6 less than twice the smaller number, find the two numbers. write and solve a system of equations for this situation

Hey there!

"The sum of two numbers is 48..." means that the two numbers will be added together and will equal 48. 

"...the larger number is 6 less than twice the smaller number..." means that if the smaller number is represented by x, the larger number will be 2x – 6, or twice the smaller number minus 6. 

The final equation will be (2x – 6) + x = 48. Now, all you need to do is simplify. 

(2x – 6) + x = 48

1(2x – 6) + 1x = 48

2x + 1x – 6 = 48

3x – 6 = 48
     + 6   + 6

3x = 54
 3      3

x = 18

So, the smaller number (x) will be be equal to 18 and the larger number (2x – 6) will be equal to (2)(18) – 6, or 30. You can check this by adding these numbers together:

18 + 30 = 48

Hope this helped you out! :-)