Multiple choice

The average of two observations, a and 12, will become c, when both the observations are doubled and one is added to each observation. The average of two observations, 5a and 16, will become d, when both the observations are doubled and one is added to each observation. What is the average of c and d?

  1. 3a + 5

  2. 3a + 10

  3. 3a + 15

  4. 3a + 20

  5. 3a + 25
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The average of a and 12 is (a+12)/2. Doubling and adding 1 gives (2a+1) and (25), so c = (2a+1+25)/2 = a+13. For 5a and 16, doubling and adding 1 gives (10a+1) and (33), so d = (10a+1+33)/2 = 5a+17. The average of c and d is (a+13+5a+17)/2 = (6a+30)/2 = 3a+15.

AI explanation

When each observation is doubled and one is added, the new average is twice the original average plus one. So c becomes 2 times the average of a and 12 plus 1, which is 2(a + 12)/2 + 1 = a + 13. Similarly, d becomes 2(5a + 16)/2 + 1 = 5a + 17. The average of c and d is (a + 13 + 5a + 17)/2 = 3a + 15.

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