When Penelope was 44 years old, her daughter was 4 times her son's age. Penelope would be twice her daughter's age when her son was 23 years old. How old would Penelope be when her son was 17 years old?
|
Penelope |
Daughter |
Son |
Before |
44 |
4 u |
1 u |
Change |
+ ? |
+ ? |
+ ? |
After |
2 p |
1 p |
23 |
The difference in the ages between Penelope and her daughter remains unchanged.
Difference in Penelope's and her daughter's ages at first
44 - 4 u = 2 p - 1 p
44 - 4 u =
1 p --- (1)
The difference in the ages between her daughter and her son remains unchanged.
Difference in her daughter's and her son's ages at first
4 u - 1 u = 1 p - 23
3 u + 23 =
1 p --- (2)
Make p the same.
(1) = (2)
44 - 4 u = 3 u + 23
3 u + 4 u = 44 - 23
7 u = 21
1 u = 21 ÷ 7 = 3
Age difference between Penelope and her son
= 44 - 1 u
= 44 - 3
= 41
Penelope's age when her son was 17 years old
= 41 + 17
= 58
Answer(s): 58