sarah is twice as old as katie. 10 years ago, the sum of their ages was 23. How old are they now
s = 2 k
s-10 + k-10 = 23
s + k = 43
2 k + k = 43
3 k = 43
k = 43/3 = 14 1/3
s = 28 2/3
To solve this problem, we can use a system of equations.
Let's assign variables to their ages. Let "S" represent Sarah's current age and "K" represent Katie's current age.
Given that Sarah is twice as old as Katie, we can write the equation: S = 2K.
We are also given information about their ages 10 years ago. We know that 10 years ago, Sarah's age was S - 10, and Katie's age was K - 10. The sum of their ages 10 years ago was 23, so we can write the equation: (S - 10) + (K - 10) = 23.
Now we have a system of two equations:
1) S = 2K
2) (S - 10) + (K - 10) = 23
To solve this system, we can substitute equation 1) into equation 2) to eliminate S:
(2K - 10) + (K - 10) = 23
3K - 20 = 23
3K = 43
K = 43/3 ≈ 14.33
Now, we can substitute the value of K back into equation 1) to find S:
S = 2(14.33)
S ≈ 28.67
Therefore, Katie is approximately 14.33 years old, and Sarah is approximately 28.67 years old.