Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 74. Give your answers in ascending order. (Eg 1, 2, 3)
- After Ethan 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 Ethan?
(a)
Total of 3 numbers
= 3 x 74
= 222
60 + 73 + 89 = 222
The 3 numbers that will give an average of 74 = 60, 73, 89
(b)
Total of 5 numbers
= 60 + 31 + 89 + 11 + 73
= 264
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
264 + 99 = 363 |
363 ÷ 6 ≈ 60.5 |
No |
264 + 98 = 362 |
362 ÷ 6 ≈ 60.3 |
No |
264 + 97 = 361 |
361 ÷ 6 ≈ 60.2 |
No |
264 + 96 = 360 |
360 ÷ 6 = 60 |
Yes |
60 ÷ 3 = 20
60 is a multiple of 3.
Highest possible 2-digit number = 96
Answer(s): (a) 60, 73, 89; (b) 96