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 Seth 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 Seth?
(a)
Total of 3 numbers
= 3 x 84
= 252
67 + 86 + 99 = 252
The 3 numbers that will give an average of 84 = 67, 86, 99
(b)
Total of 5 numbers
= 67 + 37 + 99 + 11 + 86
= 300
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
300 + 99 = 399 |
399 ÷ 6 ≈ 66.5 |
No |
300 + 98 = 398 |
398 ÷ 6 ≈ 66.3 |
No |
300 + 97 = 397 |
397 ÷ 6 ≈ 66.2 |
No |
300 + 96 = 396 |
396 ÷ 6 = 66 |
Yes |
66 ÷ 3 = 22
66 is a multiple of 3.
Highest possible 2-digit number = 96
Answer(s): (a) 67, 86, 99; (b) 96