Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 46. Give your answers in ascending order. (Eg 1, 2, 3)
- After Zeph wrote 2-digit number on the same whiteboard, the new average of the six numbers became a whole number and a multiple of 5. What was the largest possible 2-digit number written by Zeph?
(a)
Total of 3 numbers
= 3 x 46
= 138
16 + 43 + 79 = 138
The 3 numbers that will give an average of 46 = 16, 43, 79
(b)
Total of 5 numbers
= 60 + 43 + 95 + 16 + 79
= 293
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
293 + 99 = 392 |
392 ÷ 6 ≈ 65.3 |
No |
293 + 98 = 391 |
391 ÷ 6 ≈ 65.2 |
No |
293 + 97 = 390 |
390 ÷ 6 = 65 |
Yes |
65 ÷ 5 = 13
65 is a multiple of 5.
Highest possible 2-digit number = 97
Answer(s): (a) 16, 43, 79; (b) 97