SOLUTION: Leticia is 21 years older than Kate, in 2 years, Leticia will be twice as old as Kate. Find Leticia's and Katie's current age?

Question 521220: Leticia is 21 years older than Kate, in 2 years, Leticia will be twice as old as Kate. Find Leticia's and Katie's current age?
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
Let
Present age of Leticia = l
Present age of Kate = k

Leticia is 21 years older than Kate
l=k+21................(1)

In 2 years,
Leticia's age will be = l + 2
Kate's age will be = k + 2
Then,
Leticia will be twice as old as Kate.
l + 2 = 2 (k + 2)
l + 2 = 2k + 4
l = 2k + 4 - 2
l = 2k + 2 ..................(2)
Put the value of l from (1) to (2)
k + 21 = 2k + 2
k - 2k = 2 - 21
-k = -19
Multiply by -1 both sides
k = 19
Put the value of k in (1)
l=k+21
l=19+21
l = 40

Present age of Leticia = l = 40 years old
Present age of Kate = k = 19 years old

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