Ke is twice as old as Amy. Seven years ago, the sum of their ages was 31. How old is each person this year.
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To solve this problem, we can set up a system of equations based on the given information.
Let's assume Ke's age is represented by "K" and Amy's age is represented by "A."
From the problem, we know that Ke is twice as old as Amy: K = 2A. (Equation 1)
We also know that seven years ago, the sum of their ages was 31: (K-7) + (A-7) = 31. (Equation 2)
Now we can solve this system of equations to find the current ages of Ke and Amy.
Substitute the value of K from Equation 1 into Equation 2:
(2A-7) + (A-7) = 31
Combine like terms:
3A - 14 = 31
Add 14 to both sides:
3A = 45
Divide both sides by 3:
A = 15
Now, substitute the value of A (Amy's age) back into Equation 1 to find Ke's age:
K = 2A
K = 2(15)
K = 30
Therefore, Ke is 30 years old this year, and Amy is 15 years old this year.