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 Mark 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 Mark?
(a)
Total of 3 numbers
= 3 x 72
= 216
56 + 71 + 89 = 216
The 3 numbers that will give an average of 72 = 56, 71, 89
(b)
Total of 5 numbers
= 56 + 42 + 89 + 24 + 71
= 282
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
282 + 99 = 381 |
381 ÷ 6 ≈ 63.5 |
No |
282 + 98 = 380 |
380 ÷ 6 ≈ 63.3 |
No |
282 + 97 = 379 |
379 ÷ 6 ≈ 63.2 |
No |
282 + 96 = 378 |
378 ÷ 6 = 63 |
Yes |
63 ÷ 3 = 21
63 is a multiple of 3.
Highest possible 2-digit number = 96
Answer(s): (a) 56, 71, 89; (b) 96