Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 85. Give your answers in ascending order. (Eg 1, 2, 3)
- After Vincent 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 smallest possible 2-digit number written by Vincent?
(a)
Total of 3 numbers
= 3 x 85
= 255
47 + 92 + 116 = 255
The 3 numbers that will give an average of 85 = 47, 92, 116
(b)
Total of 5 numbers
= 63 + 47 + 116 + 30 + 92
= 348
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
348 + 10 = 358 |
358 ÷ 6 ≈ 59.7 |
No |
348 + 11 = 359 |
359 ÷ 6 ≈ 59.8 |
No |
348 + 12 = 360 |
360 ÷ 6 = 60 |
Yes |
60 ÷ 3 = 20
60 is a multiple of 3.
Smallest possible 2-digit number = 12
Answer(s): (a) 47, 92, 116; (b) 12