Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 49. Give your answers in ascending order. (Eg 1, 2, 3)
- After Ian wrote 2-digit number on the same whiteboard, the new average of the six numbers became a whole number and a multiple of 3. What was the largest possible 2-digit number written by Ian?
(a)
Total of 3 numbers
= 3 x 49
= 147
26 + 36 + 85 = 147
The 3 numbers that will give an average of 49 = 26, 36, 85
(b)
Total of 5 numbers
= 62 + 36 + 108 + 26 + 85
= 317
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
317 + 99 = 416 |
416 ÷ 6 ≈ 69.3 |
No |
317 + 98 = 415 |
415 ÷ 6 ≈ 69.2 |
No |
317 + 97 = 414 |
414 ÷ 6 = 69 |
Yes |
69 ÷ 3 = 23
69 is a multiple of 3.
Highest possible 2-digit number = 97
Answer(s): (a) 26, 36, 85; (b) 97