Answer:
Let's denote the present age of the daughter as "D" and the present age of the mother as "M."
According to the given information:
1. The present age of the mother is three times that of her daughter:
M = 3D
2. Five years ago, the mother's age was 7 times that of the daughter:
M - 5 = 7(D - 5)
Now we can use these two equations to solve for the present ages of the daughter and the mother.
Substitute the value of M from the first equation into the second equation:
3D - 5 = 7(D - 5)
Distribute and solve for D:
3D - 5 = 7D - 35
4D = 30
D = 30 / 4
D = 7.5
Now that we have the age of the daughter, we can use the first equation to find the age of the mother:
M = 3D
M = 3 * 7.5
M = 22.5
However, ages are typically considered whole numbers, so we need to adjust our solution.
If we assume that the daughter is 7 years old and the mother is 21 years old, then:
Present age of daughter (D) = 7 years
Present age of mother (M) = 21 years
And if you want ages in whole numbers, you can use the first equation to find other possible integer solutions. For example, if the daughter is 3 years old, the mother would be 9 years old. The specific ages would depend on the context and assumptions you make.