Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 97. Give your answers in ascending order. (Eg 1, 2, 3)
- After Zeph 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 Zeph?
(a)
Total of 3 numbers
= 3 x 97
= 291
80 + 92 + 119 = 291
The 3 numbers that will give an average of 97 = 80, 92, 119
(b)
Total of 5 numbers
= 80 + 55 + 119 + 26 + 92
= 372
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
372 + 99 = 471 |
471 ÷ 6 ≈ 78.5 |
No |
372 + 98 = 470 |
470 ÷ 6 ≈ 78.3 |
No |
372 + 97 = 469 |
469 ÷ 6 ≈ 78.2 |
No |
372 + 96 = 468 |
468 ÷ 6 = 78 |
Yes |
78 ÷ 3 = 26
78 is a multiple of 3.
Highest possible 2-digit number = 96
Answer(s): (a) 80, 92, 119; (b) 96