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 7. What was the largest possible 2-digit number written by Howard?
(a)
Total of 3 numbers
= 3 x 77
= 231
52 + 82 + 97 = 231
The 3 numbers that will give an average of 77 = 52, 82, 97
(b)
Total of 5 numbers
= 82 + 52 + 111 + 22 + 97
= 364
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
364 + 99 = 463 |
463 ÷ 6 ≈ 77.2 |
No |
364 + 98 = 462 |
462 ÷ 6 = 77 |
Yes |
77 ÷ 7 = 11
77 is a multiple of 7.
Highest possible 2-digit number = 98
Answer(s): (a) 52, 82, 97; (b) 98