When Emma was 36 years old, her daughter was 3 times her son's age. Emma would be twice her daughter's age when her son was 26 years old. How old would Emma be when her son was 14 years old?
|
Emma |
Daughter |
Son |
Before |
36 |
3 u |
1 u |
Change |
+ ? |
+ ? |
+ ? |
After |
2 p |
1 p |
26 |
The difference in the ages between Emma and her daughter remains unchanged.
Difference in Emma's and her daughter's ages at first
36 - 3 u = 2 p - 1 p
36 - 3 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
3 u - 1 u = 1 p - 26
2 u + 26 =
1 p --- (2)
Make p the same.
(1) = (2)
36 - 3 u = 2 u + 26
2 u + 3 u = 36 - 26
5 u = 10
1 u = 10 ÷ 5 = 2
Age difference between Emma and her son
= 36 - 1 u
= 36 - 2
= 34
Emma's age when her son was 14 years old
= 34 + 14
= 48
Answer(s): 48