Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 89. Give your answers in ascending order. (Eg 1, 2, 3)
- After Daniel 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 Daniel?
(a)
Total of 3 numbers
= 3 x 89
= 267
70 + 87 + 110 = 267
The 3 numbers that will give an average of 89 = 70, 87, 110
(b)
Total of 5 numbers
= 70 + 57 + 110 + 30 + 87
= 354
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
354 + 99 = 453 |
453 ÷ 6 ≈ 75.5 |
No |
354 + 98 = 452 |
452 ÷ 6 ≈ 75.3 |
No |
354 + 97 = 451 |
451 ÷ 6 ≈ 75.2 |
No |
354 + 96 = 450 |
450 ÷ 6 = 75 |
Yes |
75 ÷ 5 = 15
75 is a multiple of 5.
Highest possible 2-digit number = 96
Answer(s): (a) 70, 87, 110; (b) 96