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 Billy wrote 2-digit number on the same whiteboard, the new average of the six numbers became a whole number and a multiple of 3. What was the largest possible 2-digit number written by Billy?
(a)
Total of 3 numbers
= 3 x 60
= 180
40 + 62 + 78 = 180
The 3 numbers that will give an average of 60 = 40, 62, 78
(b)
Total of 5 numbers
= 62 + 40 + 100 + 18 + 78
= 298
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
298 + 99 = 397 |
397 ÷ 6 ≈ 66.2 |
No |
298 + 98 = 396 |
396 ÷ 6 = 66 |
Yes |
66 ÷ 3 = 22
66 is a multiple of 3.
Highest possible 2-digit number = 98
Answer(s): (a) 40, 62, 78; (b) 98