Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 36. Give your answers in ascending order. (Eg 1, 2, 3)
- After Fabian wrote 2-digit number on the same whiteboard, the new average of the six numbers became a whole number and a multiple of 5. What was the smallest possible 2-digit number written by Fabian?
(a)
Total of 3 numbers
= 3 x 36
= 108
16 + 35 + 57 = 108
The 3 numbers that will give an average of 36 = 16, 35, 57
(b)
Total of 5 numbers
= 57 + 35 + 101 + 16 + 80
= 289
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
289 + 10 = 299 |
299 ÷ 6 ≈ 49.8 |
No |
289 + 11 = 300 |
300 ÷ 6 = 50 |
Yes |
50 ÷ 5 = 10
50 is a multiple of 5.
Smallest possible 2-digit number = 11
Answer(s): (a) 16, 35, 57; (b) 11