Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 69. Give your answers in ascending order. (Eg 1, 2, 3)
- After Nick 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 Nick?
(a)
Total of 3 numbers
= 3 x 69
= 207
49 + 72 + 86 = 207
The 3 numbers that will give an average of 69 = 49, 72, 86
(b)
Total of 5 numbers
= 72 + 49 + 104 + 23 + 86
= 334
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
334 + 99 = 433 |
433 ÷ 6 ≈ 72.2 |
No |
334 + 98 = 432 |
432 ÷ 6 = 72 |
Yes |
72 ÷ 3 = 24
72 is a multiple of 3.
Highest possible 2-digit number = 98
Answer(s): (a) 49, 72, 86; (b) 98