Final answer:
The average of four consecutive odd numbers p, q, r, and s is 104. By solving the equation p + q + r + s = 416, we find that the values of p, q, r, and s are 101, 103, 105, and 107 respectively. Therefore, the sum of p and s is 208.
Step-by-step explanation:
The average of four consecutive odd numbers can be found by taking the sum of the four numbers and dividing it by 4. Let's assume that the first odd number is p, the second is q, the third is r, and the fourth is s. So, the average of p, q, r, and s is (p + q + r + s)/4.
According to the question, the average is 104. So we have the equation (p + q + r + s)/4 = 104. Multiply both sides of the equation by 4 to get p + q + r + s = 416.
Since the numbers are consecutive odd numbers, we know that they are 2 units apart from each other. So, q = p + 2, r = p + 4, and s = p + 6.
Substituting these values in the equation p + q + r + s = 416, we get p + (p + 2) + (p + 4) + (p + 6) = 416.
Simplifying the equation gives us 4p + 12 = 416. Subtracting 12 from both sides leads to 4p = 404. Dividing both sides by 4 gives us p = 101.
Therefore, the first odd number, p, is 101. The next odd numbers in the sequence would be 101 + 2, 101 + 4, and 101 + 6. So, the values of p, q, r, and s are 101, 103, 105, and 107 respectively.
The sum of p and s is 101 + 107 = 208.