Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 67. Give your answers in ascending order. (Eg 1, 2, 3)
- After Luis 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 Luis?
(a)
Total of 3 numbers
= 3 x 67
= 201
34 + 74 + 93 = 201
The 3 numbers that will give an average of 67 = 34, 74, 93
(b)
Total of 5 numbers
= 45 + 34 + 93 + 12 + 74
= 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) 34, 74, 93; (b) 12