Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 65. Give your answers in ascending order. (Eg 1, 2, 3)
- After Howard 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 Howard?
(a)
Total of 3 numbers
= 3 x 65
= 195
28 + 55 + 112 = 195
The 3 numbers that will give an average of 65 = 28, 55, 112
(b)
Total of 5 numbers
= 84 + 55 + 128 + 28 + 112
= 407
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
407 + 99 = 506 |
506 ÷ 6 ≈ 84.3 |
No |
407 + 98 = 505 |
505 ÷ 6 ≈ 84.2 |
No |
407 + 97 = 504 |
504 ÷ 6 = 84 |
Yes |
84 ÷ 3 = 28
84 is a multiple of 3.
Highest possible 2-digit number = 97
Answer(s): (a) 28, 55, 112; (b) 97