When Victoria was 38 years old, her son was 2 times her daughter's age. Victoria would be twice her son's age when her daughter was 20 years old. How old would Victoria be when her daughter was 21 years old?
|
Victoria |
Son |
Daughter |
Before |
38 |
2 u |
1 u |
Change |
+ ? |
+ ? |
+ ? |
After |
2 p |
1 p |
20 |
The difference in the ages between Victoria and her son remains unchanged.
Difference in Victoria's and her son's ages at first
38 - 2 u = 2 p - 1 p
38 - 2 u =
1 p --- (1)
The difference in the ages between her son and her daughter remains unchanged.
Difference in her son's and her daughter's ages at first
2 u - 1 u = 1 p - 20
1 u + 20 =
1 p --- (2)
Make p the same.
(1) = (2)
38 - 2 u = 1 u + 20
1 u + 2 u = 38 - 20
3 u = 18
1 u = 18 ÷ 3 = 6
Age difference between Victoria and her daughter
= 38 - 1 u
= 38 - 6
= 32
Victoria's age when her daughter was 21 years old
= 32 + 21
= 53
Answer(s): 53