Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 42. Give your answers in ascending order. (Eg 1, 2, 3)
- After Oliver 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 Oliver?
(a)
Total of 3 numbers
= 3 x 42
= 126
20 + 34 + 72 = 126
The 3 numbers that will give an average of 42 = 20, 34, 72
(b)
Total of 5 numbers
= 44 + 34 + 93 + 20 + 72
= 263
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
263 + 99 = 362 |
362 ÷ 6 ≈ 60.3 |
No |
263 + 98 = 361 |
361 ÷ 6 ≈ 60.2 |
No |
263 + 97 = 360 |
360 ÷ 6 = 60 |
Yes |
60 ÷ 3 = 20
60 is a multiple of 3.
Highest possible 2-digit number = 97
Answer(s): (a) 20, 34, 72; (b) 97