When Shannon was 46 years old, her son was 2 times her daughter's age. Shannon would be twice her son's age when her daughter was 37 years old. How old would Shannon be when her daughter was 13 years old?
|
Shannon |
Son |
Daughter |
Before |
46 |
2 u |
1 u |
Change |
+ ? |
+ ? |
+ ? |
After |
2 p |
1 p |
37 |
The difference in the ages between Shannon and her son remains unchanged.
Difference in Shannon's and her son's ages at first
46 - 2 u = 2 p - 1 p
46 - 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 - 37
1 u + 37 =
1 p --- (2)
Make p the same.
(1) = (2)
46 - 2 u = 1 u + 37
1 u + 2 u = 46 - 37
3 u = 9
1 u = 9 ÷ 3 = 3
Age difference between Shannon and her daughter
= 46 - 1 u
= 46 - 3
= 43
Shannon's age when her daughter was 13 years old
= 43 + 13
= 56
Answer(s): 56