Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 73. Give your answers in ascending order. (Eg 1, 2, 3)
- After Ivan 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 Ivan?
(a)
Total of 3 numbers
= 3 x 73
= 219
38 + 76 + 105 = 219
The 3 numbers that will give an average of 73 = 38, 76, 105
(b)
Total of 5 numbers
= 61 + 38 + 105 + 14 + 76
= 294
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
294 + 10 = 304 |
304 ÷ 6 ≈ 50.7 |
No |
294 + 11 = 305 |
305 ÷ 6 ≈ 50.8 |
No |
294 + 12 = 306 |
306 ÷ 6 = 51 |
Yes |
51 ÷ 3 = 17
51 is a multiple of 3.
Smallest possible 2-digit number = 12
Answer(s): (a) 38, 76, 105; (b) 12