Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 54. Give your answers in ascending order. (Eg 1, 2, 3)
- After Will wrote 2-digit number on the same whiteboard, the new average of the six numbers became a whole number and a multiple of 11. What was the smallest possible 2-digit number written by Will?
(a)
Total of 3 numbers
= 3 x 54
= 162
27 + 57 + 78 = 162
The 3 numbers that will give an average of 54 = 27, 57, 78
(b)
Total of 5 numbers
= 78 + 57 + 118 + 27 + 105
= 385
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
385 + 10 = 395 |
395 ÷ 6 ≈ 65.8 |
No |
385 + 11 = 396 |
396 ÷ 6 = 66 |
Yes |
66 ÷ 11 = 6
66 is a multiple of 11.
Smallest possible 2-digit number = 11
Answer(s): (a) 27, 57, 78; (b) 11