Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 50. Give your answers in ascending order. (Eg 1, 2, 3)
- After Asher 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 Asher?
(a)
Total of 3 numbers
= 3 x 50
= 150
18 + 33 + 99 = 150
The 3 numbers that will give an average of 50 = 18, 33, 99
(b)
Total of 5 numbers
= 59 + 33 + 99 + 18 + 84
= 293
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
293 + 10 = 303 |
303 ÷ 6 ≈ 50.5 |
No |
293 + 11 = 304 |
304 ÷ 6 ≈ 50.7 |
No |
293 + 12 = 305 |
305 ÷ 6 ≈ 50.8 |
No |
293 + 13 = 306 |
306 ÷ 6 = 51 |
Yes |
51 ÷ 3 = 17
51 is a multiple of 3.
Smallest possible 2-digit number = 13
Answer(s): (a) 18, 33, 99; (b) 13