Final answer:
If the daughter's age is x, then the woman's age is 10x. Using the information that in 8 years the woman will be 4 times as old as her daughter, we can solve the equation to find the daughter's age. The mother is currently 10 times the daughter's age, so she is 40 years old.
Step-by-step explanation:
Let's denote the daughter's age as x. According to the given information, the woman is 10 times as old as her daughter, so her age would be 10x. In 8 years, the woman will be 4 times as old as her daughter, so we can set up an equation:
10x + 8 = 4(x + 8)
Simplifying the equation,
10x + 8 = 4x + 32
Subtracting 4x from both sides, we get:
6x + 8 = 32
Subtracting 8 from both sides, we get:
6x = 24
Dividing both sides by 6, we get:
x = 4
Therefore, the daughter's age is 4 and the woman's age is 10 times that, which is 40. So the mother is currently 40 years old.