Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 58. 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 58
= 174
29 + 40 + 105 = 174
The 3 numbers that will give an average of 58 = 29, 40, 105
(b)
Total of 5 numbers
= 66 + 40 + 105 + 29 + 77
= 317
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
317 + 10 = 327 |
327 ÷ 6 ≈ 54.5 |
No |
317 + 11 = 328 |
328 ÷ 6 ≈ 54.7 |
No |
317 + 12 = 329 |
329 ÷ 6 ≈ 54.8 |
No |
317 + 13 = 330 |
330 ÷ 6 = 55 |
Yes |
55 ÷ 11 = 5
55 is a multiple of 11.
Smallest possible 2-digit number = 13
Answer(s): (a) 29, 40, 105; (b) 13