Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 43. 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 43
= 129
28 + 40 + 61 = 129
The 3 numbers that will give an average of 43 = 28, 40, 61
(b)
Total of 5 numbers
= 61 + 40 + 113 + 28 + 89
= 331
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
331 + 10 = 341 |
341 ÷ 6 ≈ 56.8 |
No |
331 + 11 = 342 |
342 ÷ 6 = 57 |
Yes |
57 ÷ 3 = 19
57 is a multiple of 3.
Smallest possible 2-digit number = 11
Answer(s): (a) 28, 40, 61; (b) 11