Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 89. Give your answers in ascending order. (Eg 1, 2, 3)
- After George wrote 2-digit number on the same whiteboard, the new average of the six numbers became a whole number and a multiple of 7. What was the smallest possible 2-digit number written by George?
(a)
Total of 3 numbers
= 3 x 89
= 267
50 + 101 + 116 = 267
The 3 numbers that will give an average of 89 = 50, 101, 116
(b)
Total of 5 numbers
= 78 + 50 + 116 + 21 + 101
= 366
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
366 + 10 = 376 |
376 ÷ 6 ≈ 62.7 |
No |
366 + 11 = 377 |
377 ÷ 6 ≈ 62.8 |
No |
366 + 12 = 378 |
378 ÷ 6 = 63 |
Yes |
63 ÷ 7 = 9
63 is a multiple of 7.
Smallest possible 2-digit number = 12
Answer(s): (a) 50, 101, 116; (b) 12