The sum of Lia's age and her Mother's age is 66. The difference in their ages is 28. How old are Lia and her Mother?
x - y = 28
x + y = 66
--------------- add
2 x = 94
x = 94/2
y = 66 - x
Let's find the ages of Lia and her mother step-by-step:
Step 1: Set up the equation based on the given information.
Let's say Lia's age is represented by L and her mother's age is represented by M. According to the given information, the sum of Lia's age and her mother's age is 66, so we can write the equation as:
L + M = 66
Step 2: Find the difference in their ages.
According to the given information, the difference in their ages is 28, so we can write the equation as:
M - L = 28
Step 3: Solve the system of equations.
We can solve the system of equations by using the method of substitution or elimination. Let's use the substitution method in this case.
From equation (2), we can express L in terms of M:
L = M - 28
Substituting this value of L in equation (1), we get:
(M - 28) + M = 66
2M - 28 = 66
2M = 66 + 28
2M = 94
M = 94/2
M = 47
Now substitute this value of M back into equation (1) to find L:
L + 47 = 66
L = 66 - 47
L = 19
Therefore, Lia is 19 years old and her mother is 47 years old.
To find the ages of Lia and her mother, we can set up a system of equations based on the given information.
Let's assume Lia's age is represented by 'L', and her mother's age is represented by 'M'.
From the first sentence, we know that the sum of their ages is 66.
So, the equation would be: L + M = 66. (Equation 1)
From the second sentence, we know that the difference in their ages is 28.
So, the equation would be: M - L = 28. (Equation 2)
To solve this system of equations, we can use the substitution or elimination method.
Let's use the elimination method. We'll start by multiplying Equation 2 by -1, which gives us: -M + L = -28. (Equation 3)
Now, add Equation 1 and Equation 3 together:
L + M + (-M + L) = 66 + (-28).
Simplifying the equation:
2L = 38.
Now, divide both sides of the equation by 2:
L = 19.
Substitute 19 back into Equation 1 or Equation 2 to find M:
M - 19 = 28.
M = 28 + 19.
M = 47.
So, Lia is 19 years old, and her mother is 47 years old.