Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 99. 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 5. What was the largest possible 2-digit number written by Howard?
(a)
Total of 3 numbers
= 3 x 99
= 297
73 + 103 + 121 = 297
The 3 numbers that will give an average of 99 = 73, 103, 121
(b)
Total of 5 numbers
= 73 + 57 + 121 + 30 + 103
= 384
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
384 + 99 = 483 |
483 ÷ 6 ≈ 80.5 |
No |
384 + 98 = 482 |
482 ÷ 6 ≈ 80.3 |
No |
384 + 97 = 481 |
481 ÷ 6 ≈ 80.2 |
No |
384 + 96 = 480 |
480 ÷ 6 = 80 |
Yes |
80 ÷ 5 = 16
80 is a multiple of 5.
Highest possible 2-digit number = 96
Answer(s): (a) 73, 103, 121; (b) 96