If P(t) = 30 + 5t, then P(2) + P(8) is equal to twice which P(k)?

Correct answer: P(5)

Answer: option C, P(5). First calculate the two given values: P(2) = 30 + 5(2) = 40 and P(8) = 30 + 5(8) = 70. Their sum is 40 + 70 = 110, so we need a value of P(k) equal to 55. Since P(5) = 30 + 5(5) = 55, twice P(5) is 110. There is also a useful linear-function idea: 2 and 8 are equally placed around their midpoint, because (2 + 8) / 2 = 5. For a linear function, the value at the midpoint is the average of the endpoint values, so P(2) + P(8) = 2P(5). Option A gives P(3) = 45, whose double is 90, so it fails. Option B gives P(4) = 50, whose double is 100, so it fails. Option C gives 2 × 55 = 110, so it works. Option D gives P(6) = 60, whose double is 120. Memory cue: for a linear rule, the midpoint input gives the average output.