Let the larger number be x, the smaller be y.
Equations:
9 * x = 7 * y + 186
x + y = 42
I'll start by solving the first equation for y:
y = 42 - x
Now, substituting into the first equation:
9 * x = 7 * (42 - x) + 186
9 * x = 294 - 7 * x + 186
9 * x = - 7 *x + 480
Adding 7 * x to both sides, then dividing by 16:
16 * x = 480
x = 30
Now, substituting the value of x back into the second equation:
y = 42 - 30 = 12
So x = 30, y = 12
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