Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 77. Give your answers in ascending order. (Eg 1, 2, 3)
- After Howard wrote 2-digit number on the same whiteboard, the new average of the six numbers became a whole number and a multiple of 11. What was the smallest possible 2-digit number written by Howard?
(a)
Total of 3 numbers
= 3 x 77
= 231
45 + 83 + 103 = 231
The 3 numbers that will give an average of 77 = 45, 83, 103
(b)
Total of 5 numbers
= 64 + 45 + 103 + 23 + 83
= 318
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
318 + 10 = 328 |
328 ÷ 6 ≈ 54.7 |
No |
318 + 11 = 329 |
329 ÷ 6 ≈ 54.8 |
No |
318 + 12 = 330 |
330 ÷ 6 = 55 |
Yes |
55 ÷ 11 = 5
55 is a multiple of 11.
Smallest possible 2-digit number = 12
Answer(s): (a) 45, 83, 103; (b) 12