Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 34. Give your answers in ascending order. (Eg 1, 2, 3)
- After Zeph 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 Zeph?
(a)
Total of 3 numbers
= 3 x 34
= 102
24 + 34 + 44 = 102
The 3 numbers that will give an average of 34 = 24, 34, 44
(b)
Total of 5 numbers
= 44 + 34 + 79 + 24 + 60
= 241
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
241 + 10 = 251 |
251 ÷ 6 ≈ 41.8 |
No |
241 + 11 = 252 |
252 ÷ 6 = 42 |
Yes |
42 ÷ 3 = 14
42 is a multiple of 3.
Smallest possible 2-digit number = 11
Answer(s): (a) 24, 34, 44; (b) 11