Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 60. Give your answers in ascending order. (Eg 1, 2, 3)
- After Cody 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 smallest possible 2-digit number written by Cody?
(a)
Total of 3 numbers
= 3 x 60
= 180
27 + 53 + 100 = 180
The 3 numbers that will give an average of 60 = 27, 53, 100
(b)
Total of 5 numbers
= 66 + 53 + 100 + 27 + 77
= 323
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
323 + 10 = 333 |
333 ÷ 6 ≈ 55.5 |
No |
323 + 11 = 334 |
334 ÷ 6 ≈ 55.7 |
No |
323 + 12 = 335 |
335 ÷ 6 ≈ 55.8 |
No |
323 + 13 = 336 |
336 ÷ 6 = 56 |
Yes |
56 ÷ 7 = 8
56 is a multiple of 7.
Smallest possible 2-digit number = 13
Answer(s): (a) 27, 53, 100; (b) 13