Final answer:
To find the minimum sum of one number and four times another with a product of 196, we find that the pair (14, 14) results in the smallest sum, making Option B the correct answer.
Step-by-step explanation:
To find two positive numbers whose product is 196 and for which the sum of the first number plus four times the second is a minimum, let's designate the first number as x and the second as y. So, we have:
- x × y = 196
- x + 4y is to be minimized
Since the product of x and y is 196, the possible pairs of numbers (x, y) that multiply to 196 could be (1, 196), (2, 98), (4, 49), (7, 28), and (14, 14). For each pair, we can calculate x + 4y:
- For (1, 196), we get 1 + 4(196) = 785
- For (2, 98), we get 2 + 4(98) = 394
- For (4, 49), we get 4 + 4(49) = 200
- For (7, 28), we get 7 + 4(28) = 119
- For (14, 14), we get 14 + 4(14) = 70
The pair (14, 14) provides the minimum sum of the first number and four times the second, which makes Option B the correct answer.