Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 84. Give your answers in ascending order. (Eg 1, 2, 3)
- After Xavier wrote 2-digit number on the same whiteboard, the new average of the six numbers became a whole number and a multiple of 5. What was the largest possible 2-digit number written by Xavier?
(a)
Total of 3 numbers
= 3 x 84
= 252
60 + 84 + 108 = 252
The 3 numbers that will give an average of 84 = 60, 84, 108
(b)
Total of 5 numbers
= 60 + 46 + 108 + 26 + 84
= 324
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
324 + 99 = 423 |
423 ÷ 6 ≈ 70.5 |
No |
324 + 98 = 422 |
422 ÷ 6 ≈ 70.3 |
No |
324 + 97 = 421 |
421 ÷ 6 ≈ 70.2 |
No |
324 + 96 = 420 |
420 ÷ 6 = 70 |
Yes |
70 ÷ 5 = 14
70 is a multiple of 5.
Highest possible 2-digit number = 96
Answer(s): (a) 60, 84, 108; (b) 96