Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 65. Give your answers in ascending order. (Eg 1, 2, 3)
- After Sean 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 largest possible 2-digit number written by Sean?
(a)
Total of 3 numbers
= 3 x 65
= 195
49 + 62 + 84 = 195
The 3 numbers that will give an average of 65 = 49, 62, 84
(b)
Total of 5 numbers
= 49 + 30 + 84 + 15 + 62
= 240
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
240 + 99 = 339 |
339 ÷ 6 ≈ 56.5 |
No |
240 + 98 = 338 |
338 ÷ 6 ≈ 56.3 |
No |
240 + 97 = 337 |
337 ÷ 6 ≈ 56.2 |
No |
240 + 96 = 336 |
336 ÷ 6 = 56 |
Yes |
56 ÷ 7 = 8
56 is a multiple of 7.
Highest possible 2-digit number = 96
Answer(s): (a) 49, 62, 84; (b) 96