Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 38. Give your answers in ascending order. (Eg 1, 2, 3)
- After Tim 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 Tim?
(a)
Total of 3 numbers
= 3 x 38
= 114
26 + 39 + 49 = 114
The 3 numbers that will give an average of 38 = 26, 39, 49
(b)
Total of 5 numbers
= 49 + 39 + 77 + 26 + 62
= 253
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
253 + 10 = 263 |
263 ÷ 6 ≈ 43.8 |
No |
253 + 11 = 264 |
264 ÷ 6 = 44 |
Yes |
44 ÷ 11 = 4
44 is a multiple of 11.
Smallest possible 2-digit number = 11
Answer(s): (a) 26, 39, 49; (b) 11