Final answer:
To find the two positive numbers, we can set up a system of equations and solve for the values. The larger of the two numbers is approximately 41.33.
Step-by-step explanation:
To find the two positive numbers, let's assume the first number is x and the second number is y. According to the given information, the sum of the first number and twice the second number is equal to 124, so we can write the equation as:
x + 2y = 124
Next, we need to find the product of these two numbers. The product of two numbers is maximum when they are equal. Therefore, we can write another equation:
x = y
Now, we can substitute the value of x in the first equation:
y + 2y = 124
3y = 124
y = 41.33
The larger of the two numbers is y, which is approximately 41.33. Rounding it up to the nearest whole number, the larger number is 42.