Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 30. Give your answers in ascending order. (Eg 1, 2, 3)
- After Tim wrote 2-digit number on the same whiteboard, the new average of the six numbers became a whole number and a multiple of 5. What was the smallest possible 2-digit number written by Tim?
(a)
Total of 3 numbers
= 3 x 30
= 90
16 + 26 + 48 = 90
The 3 numbers that will give an average of 30 = 16, 26, 48
(b)
Total of 5 numbers
= 48 + 26 + 78 + 16 + 61
= 229
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
229 + 10 = 239 |
239 ÷ 6 ≈ 39.8 |
No |
229 + 11 = 240 |
240 ÷ 6 = 40 |
Yes |
40 ÷ 5 = 8
40 is a multiple of 5.
Smallest possible 2-digit number = 11
Answer(s): (a) 16, 26, 48; (b) 11