Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 64. Give your answers in ascending order. (Eg 1, 2, 3)
- After Tim 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 Tim?
(a)
Total of 3 numbers
= 3 x 64
= 192
45 + 66 + 81 = 192
The 3 numbers that will give an average of 64 = 45, 66, 81
(b)
Total of 5 numbers
= 66 + 45 + 100 + 24 + 81
= 316
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
316 + 99 = 415 |
415 ÷ 6 ≈ 69.2 |
No |
316 + 98 = 414 |
414 ÷ 6 = 69 |
Yes |
69 ÷ 3 = 23
69 is a multiple of 3.
Highest possible 2-digit number = 98
Answer(s): (a) 45, 66, 81; (b) 98