When Shiyun was 48 years old, her son was 5 times her daughter's age. Shiyun would be twice her son's age when her daughter was 30 years old. How old would Shiyun be when her daughter was 18 years old?
|
Shiyun |
Son |
Daughter |
Before |
48 |
5 u |
1 u |
Change |
+ ? |
+ ? |
+ ? |
After |
2 p |
1 p |
30 |
The difference in the ages between Shiyun and her son remains unchanged.
Difference in Shiyun's and her son's ages at first
48 - 5 u = 2 p - 1 p
48 - 5 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
5 u - 1 u = 1 p - 30
4 u + 30 =
1 p --- (2)
Make p the same.
(1) = (2)
48 - 5 u = 4 u + 30
4 u + 5 u = 48 - 30
9 u = 18
1 u = 18 ÷ 9 = 2
Age difference between Shiyun and her daughter
= 48 - 1 u
= 48 - 2
= 46
Shiyun's age when her daughter was 18 years old
= 46 + 18
= 64
Answer(s): 64