Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 48. Give your answers in ascending order. (Eg 1, 2, 3)
- After Brandon 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 Brandon?
(a)
Total of 3 numbers
= 3 x 48
= 144
29 + 43 + 72 = 144
The 3 numbers that will give an average of 48 = 29, 43, 72
(b)
Total of 5 numbers
= 62 + 43 + 93 + 29 + 72
= 299
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
299 + 99 = 398 |
398 ÷ 6 ≈ 66.3 |
No |
299 + 98 = 397 |
397 ÷ 6 ≈ 66.2 |
No |
299 + 97 = 396 |
396 ÷ 6 = 66 |
Yes |
66 ÷ 3 = 22
66 is a multiple of 3.
Highest possible 2-digit number = 97
Answer(s): (a) 29, 43, 72; (b) 97