The difference of two numbers is 15. the larger number is 1 more than 3 times the smaller number. find the two numbers.

Let the smaller number be x.

The larger number is 1 more than 3 times the smaller number; in numbers this is: 3x + 1.

Their sum is 15, so subtracting x from 3x + 1 will be equal to 15. Your equation is: 15 = (3x + 1) - x

Solve 15 = (3x + 1) - x algebraically for x, and then plug x into 3x + 1 to find the larger number.

15 = (3x + 1) - x
15 = 3x + 1 - x
15 = 2x + 1
14 = 2x
7 = x

3x + 1
3(7) + 1
21 + 1
22

Finally, check all work.

22 - 7 = 15
7(3) + 1 = 22

The smaller number is 7 and the larger number is 22.