Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 47. Give your answers in ascending order. (Eg 1, 2, 3)
- After Sam 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 Sam?
(a)
Total of 3 numbers
= 3 x 47
= 141
21 + 49 + 71 = 141
The 3 numbers that will give an average of 47 = 21, 49, 71
(b)
Total of 5 numbers
= 71 + 49 + 113 + 21 + 95
= 349
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
349 + 10 = 359 |
359 ÷ 6 ≈ 59.8 |
No |
349 + 11 = 360 |
360 ÷ 6 = 60 |
Yes |
60 ÷ 5 = 12
60 is a multiple of 5.
Smallest possible 2-digit number = 11
Answer(s): (a) 21, 49, 71; (b) 11