Five numbers were written on the whiteboard as shown:
- Write down the 3 numbers that will give an average of 38. Give your answers in ascending order. (Eg 1, 2, 3)
- After Jenson 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 Jenson?
(a)
Total of 3 numbers
= 3 x 38
= 114
14 + 42 + 58 = 114
The 3 numbers that will give an average of 38 = 14, 42, 58
(b)
Total of 5 numbers
= 58 + 42 + 93 + 14 + 76
= 283
Total of 6 numbers |
Average of 6 numbers |
Is it a whole number? |
283 + 10 = 293 |
293 ÷ 6 ≈ 48.8 |
No |
283 + 11 = 294 |
294 ÷ 6 = 49 |
Yes |
49 ÷ 7 = 7
49 is a multiple of 7.
Smallest possible 2-digit number = 11
Answer(s): (a) 14, 42, 58; (b) 11