Lily is 14 years older than her brother Ezekiel. In 8 years she will be twice as old as Ezekiel will be then. What is their current and future age?
brother's age ---- x
Lily's age ------- x+ 14
8 years from now:
brother's age = x+8
Lily's age = x+14 + 8 = x + 22
x+22 = 2(x+8)
solve for x and sub into my definitions
To solve this problem, we can start by setting up equations based on the given information.
Let's assume Lily's current age is L and Ezekiel's current age is E.
From the problem statement, we know that Lily is 14 years older than Ezekiel:
L = E + 14
In 8 years, Lily will be (L + 8) years old, and Ezekiel will be (E + 8) years old. It is given that Lily will be twice as old as Ezekiel then:
L + 8 = 2(E + 8)
Now we have a system of two equations:
L = E + 14 ----(1)
L + 8 = 2(E + 8) ----(2)
We can solve this system of equations to find the values of L and E.
Substituting equation (1) into equation (2):
(E + 14) + 8 = 2(E + 8)
E + 22 = 2E + 16
Subtracting E from both sides:
22 = E + 16
Subtracting 16 from both sides:
6 = E
Now we can substitute the value of E back into equation (1) to find Lily's current age:
L = E + 14
L = 6 + 14
L = 20
Therefore, currently Lily is 20 years old and Ezekiel is 6 years old.
In 8 years, Lily will be 28 and Ezekiel will be 14.