Rowena is now half as her mother. 8 years ago, she was 1/3 as old. Find their ages.
So is the half 1/2x or x/2?
same thing
e.g. (1/2)(12) = 6
12/2 = 6
as to your question,
mom's age ---- x
Rowena's age -- x/2
8 years ago:
mom ---- x-8
Rowena -- x/2 - 8
x/2 - 8 = (1/3)(x-8)
times 6, the LCD
3x - 48 = 2(x-8)
3x - 48 = 2x - 16
x = 32
Mom is 32, Rowena is 16
check:
8 years ago, the mom was 24
Rowena was 8, which is 1/3 of 24
(mmmhh, so Mom had Rowena when she was 16 ? Not a suitable question.)
same thing
e.g. (1/2)(12) = 6
12/2 = 6
as to your question,
mom's age ---- x
Rowena's age -- x/2
8 years ago:
mom ---- x-8
Rowena -- x/2 - 8
x/2 - 8 = (1/3)(x-8)
times 6, the LCD
3x - 48 = 2(x-8)
3x - 48 = 2x - 16
x = 32
Mom is 32, Rowena is 16
check:
8 years ago, the mom was 24
Rowena was 8, which is 1/3 of 24
In this problem, we are given information about Rowena's age and her relationship to her mother's age. Let's solve it step by step.
Let's assume Rowena's current age is represented by the variable "x." According to the problem, Rowena is now half as old as her mother. Since we don't have the age of Rowena's mother, let's represent her age as "M," using the variable "M."
So, according to the given information, we can write the equation: x = M/2
Next, the problem states that 8 years ago, Rowena was 1/3 as old. To calculate Rowena's age 8 years ago, we subtract 8 from the current age "x."
Rowena's age 8 years ago is represented by "x - 8." According to the problem, this age is equal to 1/3 of her mother's age 8 years ago, which is represented by "M - 8/3."
So, we can write another equation: x - 8 = (M - 8)/3
Now we have a system of two equations:
1) x = M/2
2) x - 8 = (M - 8)/3
To find the ages of Rowena and her mother, we can solve this system of equations.
One possible approach is substitution. From the first equation, we have M = 2x. Substituting this value into the second equation, we get:
x - 8 = (2x - 8)/3
To eliminate the fraction, we can multiply both sides of the equation by 3:
3(x - 8) = 2x - 8
Expanding the equation:
3x - 24 = 2x - 8
Bringing like terms to one side:
3x - 2x = 24 - 8
x = 16
Now that we have the value of x, we can substitute it back into the first equation to find M:
M = 2x
M = 2 * 16
M = 32
So, Rowena's current age is 16, and her mother's current age is 32.