A woman is four times as old as her son. In 5 years' time, she will be three times as old as her son. How old is the woman?
To solve this problem, let's assign variables to represent the ages of the woman and her son.
Let's say the son's age is S years.
According to the problem, the woman is four times as old as her son, so her age can be represented as 4S.
In 5 years' time, the son's age will be (S + 5), and the woman's age will be (4S + 5).
According to the problem, in 5 years' time, the woman's age will be three times as old as her son, so we can set up the following equation:
4S + 5 = 3(S + 5)
Now let's solve the equation:
4S + 5 = 3S + 15
4S - 3S = 15 - 5
S = 10
So, the son's age is 10 years.
Now, let's find the woman's age:
Woman's age = 4S
Woman's age = 4 * 10
Woman's age = 40
Therefore, the woman is 40 years old.
w = 4s
w+5 = 3(s+5)
-------------------
4s+5 = 3s+15
s = 10
so she is 40 and her son is 10
in 5 years, she will be 45, and the son will be 15.
45 = 3*15
Therefore, the woman is 40 years old.
To solve this problem, let's use algebra.
Let's assume the woman's age is represented by "W" and her son's age is represented by "S".
According to the problem, the woman is four times as old as her son. This can be written as:
W = 4S ---(1)
In 5 years' time, the woman will be three times as old as her son. We can represent this as:
W + 5 = 3(S + 5) ---(2)
To find the woman's age, we need to solve this system of equations.
Substituting equation (1) into equation (2), we get:
4S + 5 = 3(S + 5)
Simplifying this equation gives us:
4S + 5 = 3S + 15
Subtracting 3S from both sides gives:
4S - 3S + 5 = 15
Simplifying further, we have:
S + 5 = 15
Subtracting 5 from both sides gives:
S = 15 - 5
Simplifying further, we have:
S = 10
Now that we have the son's age, we can substitute this value back into equation (1) to find the woman's age:
W = 4S
W = 4(10)
W = 40
Therefore, the woman is 40 years old.