Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 49. Give your answers in ascending order. (Eg 1, 2, 3)
- After Pierre 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 Pierre?
(a)
Total of 3 numbers
= 3 x 49
= 147
11 + 35 + 101 = 147
The 3 numbers that will give an average of 49 = 11, 35, 101
(b)
Total of 5 numbers
= 54 + 35 + 101 + 11 + 80
= 281
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
281 + 10 = 291 |
291 ÷ 6 ≈ 48.5 |
No |
281 + 11 = 292 |
292 ÷ 6 ≈ 48.7 |
No |
281 + 12 = 293 |
293 ÷ 6 ≈ 48.8 |
No |
281 + 13 = 294 |
294 ÷ 6 = 49 |
Yes |
49 ÷ 7 = 7
49 is a multiple of 7.
Smallest possible 2-digit number = 13
Answer(s): (a) 11, 35, 101; (b) 13