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 Liam 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 Liam?
(a)
Total of 3 numbers
= 3 x 54
= 162
32 + 51 + 79 = 162
The 3 numbers that will give an average of 54 = 32, 51, 79
(b)
Total of 5 numbers
= 51 + 32 + 89 + 11 + 79
= 262
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
262 + 99 = 361 |
361 ÷ 6 ≈ 60.2 |
No |
262 + 98 = 360 |
360 ÷ 6 = 60 |
Yes |
60 ÷ 5 = 12
60 is a multiple of 5.
Highest possible 2-digit number = 98
Answer(s): (a) 32, 51, 79; (b) 98