When Anna was 45 years old, her daughter was 5 times her son's age. Anna would be twice her daughter's age when her son was 27 years old. How old would Anna be when her son was 14 years old?
|
Anna |
Daughter |
Son |
Before |
45 |
5 u |
1 u |
Change |
+ ? |
+ ? |
+ ? |
After |
2 p |
1 p |
27 |
The difference in the ages between Anna and her daughter remains unchanged.
Difference in Anna's and her daughter's ages at first
45 - 5 u = 2 p - 1 p
45 - 5 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
5 u - 1 u = 1 p - 27
4 u + 27 =
1 p --- (2)
Make p the same.
(1) = (2)
45 - 5 u = 4 u + 27
4 u + 5 u = 45 - 27
9 u = 18
1 u = 18 ÷ 9 = 2
Age difference between Anna and her son
= 45 - 1 u
= 45 - 2
= 43
Anna's age when her son was 14 years old
= 43 + 14
= 57
Answer(s): 57