Let's call the smaller number "x" and the larger number "y."
According to the information given:
1. The sum of the two numbers is 191, so we can write the equation:
x + y = 191
2. One number (y) is 51 more than the other (x), which can be written as:
y = x + 51
Now, we can use these two equations to solve for x and y.
First, substitute the expression for y from the second equation into the first equation:
x + (x + 51) = 191
Now, combine like terms:
2x + 51 = 191
Subtract 51 from both sides:
2x = 191 - 51
2x = 140
Divide by 2:
x = 140 / 2
x = 70
Now that we've found the value of x, we can find y using the second equation:
y = x + 51
y = 70 + 51
y = 121
So, the smaller number (x) is 70, and the larger number (y) is 121.