Jill and Bill are two members of the Hill family. Jill is 8 years old and Bill is 9 years old. What will Bill's age be when the total of the digits in both their ages is once again 17?
1+8+x + 1+9+x = 10+10+17
2x = 18
x=9
17,18
To find out what Bill's age will be when the total of the digits in both their ages is once again 17, we need to determine the possible combinations of their ages that would add up to 17.
First, let's see what possible combinations of digits can add up to 17:
- 1 + 6 = 7
- 2 + 5 = 7
- 3 + 4 = 7
- 1 + 7 = 8
- 2 + 6 = 8
- 3 + 5 = 8
- 4 + 4 = 8
- 1 + 8 = 9
- 2 + 7 = 9
- 3 + 6 = 9
- 4 + 5 = 9
- 2 + 8 = 10
- 3 + 7 = 10
- 4 + 6 = 10
- 3 + 8 = 11
- 4 + 7 = 11
- 5 + 6 = 11
- 4 + 8 = 12
- 5 + 7 = 12
- 6 + 6 = 12
- 5 + 8 = 13
- 6 + 7 = 13
- 6 + 8 = 14
- 7 + 7 = 14
- 7 + 8 = 15
- 8 + 8 = 16
Since Jill is 8 years old, her age can't be part of the combination because Bill will have to take that number. Additionally, Jill's age cannot be 7 or 9 since Bill's age cannot be equal to or younger than Jill's age.
From the list above, the only possible combination is 8 + 9 = 17. Since Bill's age is 9, it means that Bill's age will remain 9 when the total of the digits in both their ages is once again 17.