Question

How can the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 be placed in the 10 blanks shown below so that each number is used exactly once in order to maximize the value of P?

P = (_ + _ + _ + _ +_) (_ + _ + _ + _ +_)

Answer 1

To maximize the value of P, place the highest numbers in the first set of blanks and the lowest numbers in the second set. The numbers should be placed as follows: 6, 7, 8, 9, 10 in the first set and 1, 2, 3, 4, 5 in the second set.

Step-by-step explanation:

To maximize the value of P, we need to place the highest numbers in the first set of blanks and the lowest numbers in the second set of blanks. So, we can place the numbers 6, 7, 8, 9, and 10 in the first set of blanks and the numbers 1, 2, 3, 4, and 5 in the second set of blanks.

That gives us the following: P = (6 + 7 + 8 + 9 + 10) (1 + 2 + 3 + 4 + 5)

Simplifying the expression, we get P = 40 × 15 = 600.

Therefore, to maximize the value of P, the numbers should be placed as follows: 6, 7, 8, 9, 10 in the first set and 1, 2, 3, 4, 5 in the second set.