Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 51. Give your answers in ascending order. (Eg 1, 2, 3)
- After Reggie 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 Reggie?
(a)
Total of 3 numbers
= 3 x 51
= 153
25 + 37 + 91 = 153
The 3 numbers that will give an average of 51 = 25, 37, 91
(b)
Total of 5 numbers
= 67 + 37 + 103 + 25 + 91
= 323
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
323 + 99 = 422 |
422 ÷ 6 ≈ 70.3 |
No |
323 + 98 = 421 |
421 ÷ 6 ≈ 70.2 |
No |
323 + 97 = 420 |
420 ÷ 6 = 70 |
Yes |
70 ÷ 7 = 10
70 is a multiple of 7.
Highest possible 2-digit number = 97
Answer(s): (a) 25, 37, 91; (b) 97