Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 55. Give your answers in ascending order. (Eg 1, 2, 3)
- After Cody 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 Cody?
(a)
Total of 3 numbers
= 3 x 55
= 165
35 + 53 + 77 = 165
The 3 numbers that will give an average of 55 = 35, 53, 77
(b)
Total of 5 numbers
= 53 + 35 + 91 + 24 + 77
= 280
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
280 + 99 = 379 |
379 ÷ 6 ≈ 63.2 |
No |
280 + 98 = 378 |
378 ÷ 6 = 63 |
Yes |
63 ÷ 3 = 21
63 is a multiple of 3.
Highest possible 2-digit number = 98
Answer(s): (a) 35, 53, 77; (b) 98