Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 54. Give your answers in ascending order. (Eg 1, 2, 3)
- After Ryan 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 Ryan?
(a)
Total of 3 numbers
= 3 x 54
= 162
22 + 46 + 94 = 162
The 3 numbers that will give an average of 54 = 22, 46, 94
(b)
Total of 5 numbers
= 73 + 46 + 118 + 22 + 94
= 353
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
353 + 99 = 452 |
452 ÷ 6 ≈ 75.3 |
No |
353 + 98 = 451 |
451 ÷ 6 ≈ 75.2 |
No |
353 + 97 = 450 |
450 ÷ 6 = 75 |
Yes |
75 ÷ 3 = 25
75 is a multiple of 3.
Highest possible 2-digit number = 97
Answer(s): (a) 22, 46, 94; (b) 97