Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 45. Give your answers in ascending order. (Eg 1, 2, 3)
- After John 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 John?
(a)
Total of 3 numbers
= 3 x 45
= 135
11 + 28 + 96 = 135
The 3 numbers that will give an average of 45 = 11, 28, 96
(b)
Total of 5 numbers
= 47 + 28 + 96 + 11 + 75
= 257
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
257 + 10 = 267 |
267 ÷ 6 ≈ 44.5 |
No |
257 + 11 = 268 |
268 ÷ 6 ≈ 44.7 |
No |
257 + 12 = 269 |
269 ÷ 6 ≈ 44.8 |
No |
257 + 13 = 270 |
270 ÷ 6 = 45 |
Yes |
45 ÷ 3 = 15
45 is a multiple of 3.
Smallest possible 2-digit number = 13
Answer(s): (a) 11, 28, 96; (b) 13