There are three numbers whos sum is 45. The ratio of the sum of the first two numbers to the third number is 8/7. The difference between the first number and the second number is 8. Find the three numbers.

x+y+z=45.

(x+y)/z=8/7.

x-y=8.

susbtitute  form equation 1 x+y=45-z in equation 2.

(45-z)/z =8/7.

8z=7(45-z).

8z+7z=7*45.

z=7*45/15=21.

x+y=45-z=45-21=24.

Now solve

x+y=24.

x-y =8.

By adding 2x=32.

x=32/2 =16.

y=24-x=24-16=8.

The numbers are 16,8,21.