Question

The age of a woman is four times the age of her daughter. Five years from now, the age of the woman will be three times the age of her daughter. What is the present age of the daughter?

A) 2 years
B) 3 years
C) 5 years
D) 10 years

Answer 1

By setting up a system of equations using the information given, we can solve for the present age of the daughter, which is determined to be 10 years.

Step-by-step explanation:

To determine the present age of the daughter, we need to set up a system of equations based on the information given. Let's denote the present age of the woman as w and the present age of the daughter as d.

From the problem, we know that:

1. w = 4d (The age of the woman is four times the age of her daughter)
2. w + 5 = 3(d + 5) (Five years from now, the woman's age will be three times the age of her daughter)

Substituting the first equation into the second gives us:

4d + 5 = 3(d + 5)

Expanding the second equation, we get:

4d + 5 = 3d + 15

Now, let's solve for d:

4d - 3d = 15 - 5

d = 10

Thus, the present age of the daughter is 10 years.