Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 37. Give your answers in ascending order. (Eg 1, 2, 3)
- After Eric 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 Eric?
(a)
Total of 3 numbers
= 3 x 37
= 111
19 + 39 + 53 = 111
The 3 numbers that will give an average of 37 = 19, 39, 53
(b)
Total of 5 numbers
= 53 + 39 + 82 + 19 + 66
= 259
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
259 + 10 = 269 |
269 ÷ 6 ≈ 44.8 |
No |
259 + 11 = 270 |
270 ÷ 6 = 45 |
Yes |
45 ÷ 3 = 15
45 is a multiple of 3.
Smallest possible 2-digit number = 11
Answer(s): (a) 19, 39, 53; (b) 11