let 'x' and 'y' represent the numbers:

the sum of two positive numbers is 36:

x + y = 36

y = 36 - x

twice the first number added to their product is 224:

2x + xy = 224

plug y = 36 - x into the last equation:

2x + x(36 - x) = 224

by solving we find:

x1 = 30.7

x2 = 7.3

click here to see the step by step solution of the equation:

for x = 30.7 we have y = 36 - 30.7 = 5.3

for x = 7.3 we have y = 36 - 7.3 = 28.7

there are two solutions: (30.7, 5.3) and (7.3, 28.7).