Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 61. Give your answers in ascending order. (Eg 1, 2, 3)
- After Perry 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 Perry?
(a)
Total of 3 numbers
= 3 x 61
= 183
29 + 54 + 100 = 183
The 3 numbers that will give an average of 61 = 29, 54, 100
(b)
Total of 5 numbers
= 68 + 54 + 100 + 29 + 78
= 329
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
329 + 10 = 339 |
339 ÷ 6 ≈ 56.5 |
No |
329 + 11 = 340 |
340 ÷ 6 ≈ 56.7 |
No |
329 + 12 = 341 |
341 ÷ 6 ≈ 56.8 |
No |
329 + 13 = 342 |
342 ÷ 6 = 57 |
Yes |
57 ÷ 3 = 19
57 is a multiple of 3.
Smallest possible 2-digit number = 13
Answer(s): (a) 29, 54, 100; (b) 13