When Sarah was 49 years old, her son was 5 times her daughter's age. Sarah would be twice her son's age when her daughter was 22 years old. How old would Sarah be when her daughter was 2 years old?
|
Sarah |
Son |
Daughter |
Before |
49 |
5 u |
1 u |
Change |
+ ? |
+ ? |
+ ? |
After |
2 p |
1 p |
22 |
The difference in the ages between Sarah and her son remains unchanged.
Difference in Sarah's and her son's ages at first
49 - 5 u = 2 p - 1 p
49 - 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 - 22
4 u + 22 =
1 p --- (2)
Make p the same.
(1) = (2)
49 - 5 u = 4 u + 22
4 u + 5 u = 49 - 22
9 u = 27
1 u = 27 ÷ 9 = 3
Age difference between Sarah and her daughter
= 49 - 1 u
= 49 - 3
= 46
Sarah's age when her daughter was 2 years old
= 46 + 2
= 48
Answer(s): 48