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 Seth 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 largest possible 2-digit number written by Seth?
(a)
Total of 3 numbers
= 3 x 49
= 147
19 + 42 + 86 = 147
The 3 numbers that will give an average of 49 = 19, 42, 86
(b)
Total of 5 numbers
= 60 + 42 + 110 + 19 + 86
= 317
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
317 + 99 = 416 |
416 ÷ 6 ≈ 69.3 |
No |
317 + 98 = 415 |
415 ÷ 6 ≈ 69.2 |
No |
317 + 97 = 414 |
414 ÷ 6 = 69 |
Yes |
69 ÷ 3 = 23
69 is a multiple of 3.
Highest possible 2-digit number = 97
Answer(s): (a) 19, 42, 86; (b) 97