Final answer:
To find the two positive numbers whose product is 192 and for which the sum of the first number plus three times the second number is minimal, we compute the sum for each given option. The pair of numbers 12 and 16 not only multiply to make 192 but also produce the minimum sum of 60, thus satisfying the requirements.
Step-by-step explanation:
The problem is asking to find two positive numbers whose product is 192 and for which the sum of the first number plus three times the second number is minimal. We can systematically evaluate each of the given options (a-d) to determine which pair of numbers meets these requirements.
Option a: 12 and 16 multiply to 192, and 12 + 3(16) = 12 + 48 = 60.
Option b: 8 and 24 also multiply to 192, and 8 + 3(24) = 8 + 72 = 80.
Option c: 6 and 32 multiply to 192, and 6 + 3(32) = 6 + 96 = 102.
Option d: 4 and 48 multiply to 192, and 4 + 3(48) = 4 + 144 = 148.
The minimum sum is achieved with option a, where the sum is 60. Therefore, the two positive numbers that satisfy the given requirements are 12, 16.