Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 39. Give your answers in ascending order. (Eg 1, 2, 3)
- After Neave 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 smallest possible 2-digit number written by Neave?
(a)
Total of 3 numbers
= 3 x 39
= 117
20 + 39 + 58 = 117
The 3 numbers that will give an average of 39 = 20, 39, 58
(b)
Total of 5 numbers
= 58 + 39 + 88 + 20 + 72
= 277
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
277 + 10 = 287 |
287 ÷ 6 ≈ 47.8 |
No |
277 + 11 = 288 |
288 ÷ 6 = 48 |
Yes |
48 ÷ 3 = 16
48 is a multiple of 3.
Smallest possible 2-digit number = 11
Answer(s): (a) 20, 39, 58; (b) 11