Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 58. Give your answers in ascending order. (Eg 1, 2, 3)
- After Sean 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 Sean?
(a)
Total of 3 numbers
= 3 x 58
= 174
24 + 52 + 98 = 174
The 3 numbers that will give an average of 58 = 24, 52, 98
(b)
Total of 5 numbers
= 69 + 52 + 128 + 24 + 98
= 371
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
371 + 99 = 470 |
470 ÷ 6 ≈ 78.3 |
No |
371 + 98 = 469 |
469 ÷ 6 ≈ 78.2 |
No |
371 + 97 = 468 |
468 ÷ 6 = 78 |
Yes |
78 ÷ 3 = 26
78 is a multiple of 3.
Highest possible 2-digit number = 97
Answer(s): (a) 24, 52, 98; (b) 97