Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 65. Give your answers in ascending order. (Eg 1, 2, 3)
- After Zane 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 Zane?
(a)
Total of 3 numbers
= 3 x 65
= 195
33 + 68 + 94 = 195
The 3 numbers that will give an average of 65 = 33, 68, 94
(b)
Total of 5 numbers
= 45 + 33 + 94 + 18 + 68
= 258
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
258 + 10 = 268 |
268 ÷ 6 ≈ 44.7 |
No |
258 + 11 = 269 |
269 ÷ 6 ≈ 44.8 |
No |
258 + 12 = 270 |
270 ÷ 6 = 45 |
Yes |
45 ÷ 3 = 15
45 is a multiple of 3.
Smallest possible 2-digit number = 12
Answer(s): (a) 33, 68, 94; (b) 12