Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 72. Give your answers in ascending order. (Eg 1, 2, 3)
- After Albert wrote 2-digit number on the same whiteboard, the new average of the six numbers became a whole number and a multiple of 11. What was the largest possible 2-digit number written by Albert?
(a)
Total of 3 numbers
= 3 x 72
= 216
49 + 69 + 98 = 216
The 3 numbers that will give an average of 72 = 49, 69, 98
(b)
Total of 5 numbers
= 69 + 49 + 124 + 24 + 98
= 364
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
364 + 99 = 463 |
463 ÷ 6 ≈ 77.2 |
No |
364 + 98 = 462 |
462 ÷ 6 = 77 |
Yes |
77 ÷ 11 = 7
77 is a multiple of 11.
Highest possible 2-digit number = 98
Answer(s): (a) 49, 69, 98; (b) 98