Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 47. Give your answers in ascending order. (Eg 1, 2, 3)
- After Caden 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 Caden?
(a)
Total of 3 numbers
= 3 x 47
= 141
25 + 43 + 73 = 141
The 3 numbers that will give an average of 47 = 25, 43, 73
(b)
Total of 5 numbers
= 57 + 43 + 83 + 25 + 73
= 281
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
281 + 99 = 380 |
380 ÷ 6 ≈ 63.3 |
No |
281 + 98 = 379 |
379 ÷ 6 ≈ 63.2 |
No |
281 + 97 = 378 |
378 ÷ 6 = 63 |
Yes |
63 ÷ 7 = 9
63 is a multiple of 7.
Highest possible 2-digit number = 97
Answer(s): (a) 25, 43, 73; (b) 97