the sum of two numbers is 61. if the larger number is seven less than three times the smaller number, find both numbers

Let x=the larger number, and let y=the smaller number. From the information given, we can get:

x+y=61

x+7=3y

Subtracting the first equation from the second one, we get:

7-y=3y-61

-4y=-68

y=17

Substituting y into the first equation, we get:

x+y=61

x+17=61

x=44

Therefore, the larger number is 44 and the smaller number is 17.