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 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 48
= 144
25 + 54 + 65 = 144
The 3 numbers that will give an average of 48 = 25, 54, 65
(b)
Total of 5 numbers
= 54 + 25 + 85 + 15 + 65
= 244
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
244 + 99 = 343 |
343 ÷ 6 ≈ 57.2 |
No |
244 + 98 = 342 |
342 ÷ 6 = 57 |
Yes |
57 ÷ 3 = 19
57 is a multiple of 3.
Highest possible 2-digit number = 98
Answer(s): (a) 25, 54, 65; (b) 98