J = 2/3 * L
J-6 = (L-6) - 20
2 L/3 = 6 + L -26
2 L/3 - 3 L/3 = - 20
- L/3 = -20
L = 60
J = 40
J-6 = 34
L-6 = 54
J-6 = (L-6) - 20
2 L/3 = 6 + L -26
2 L/3 - 3 L/3 = - 20
- L/3 = -20
L = 60
J = 40
J-6 = 34
L-6 = 54
Let x represent Lyn's current age.
According to the given information, Joy is 2/3 as old as Lyn. Therefore, Joy's current age can be represented as (2/3)x.
Now, six years ago, Joy's age would have been (2/3)x - 6, and Lyn's age would have been x - 6.
It is also given that, six years ago, Joy's age was 20 less than Lyn's age.
Using this information, we can set up the equation:
(2/3)x - 6 = (x - 6) - 20
Now, let's solve for x to find Lyn's current age.
(2/3)x - 6 = x - 6 - 20
Multiply through by 3 to eliminate the fraction:
2x - 18 = 3x - 6 - 60
Combine like terms:
2x - 18 = 3x - 66
Subtract 2x from both sides:
-18 = x - 66
Add 66 to both sides:
48 = x
Therefore, Lyn's current age is 48 years old.
Now, let's find Joy's current age by substituting the value of x back into the equation.
Joy's current age = (2/3)x = (2/3)(48) = 32 years old.
Finally, let's determine their ages six years ago.
Six years ago, Lyn's age = 48 - 6 = 42 years old.
Six years ago, Joy's age = 32 - 6 = 26 years old.
Therefore, six years ago, Lyn was 42 years old, and Joy was 26 years old.
Let J represent Joy's current age, and L represent Lyn's current age.
Given that "Joy is 2/3 as old as Lyn," we can express this as an equation:
J = (2/3)L
The second piece of information states that "Six years ago, Joy is 20 less than Lyn's age."
We need to subtract 6 from both J and L, and write an equation:
J - 6 = L - 6 - 20
Now, we can solve the system of equations simultaneously to find the ages of Joy and Lyn six years ago.
Simplifying the equations:
J = (2/3)L
J - 6 = L - 26
To solve the system, we can substitute the value of J from the first equation into the second equation:
(2/3)L - 6 = L - 26
Multiplying the entire equation by 3 to eliminate the fractions:
2L - 18 = 3L - 78
Moving all the related terms to one side:
3L - 2L = 78 - 18
L = 60
Now that we know the value of L, we can substitute it back into the first equation to find J:
J = (2/3) * 60
J = 40
Therefore, six years ago, Joy was 40 - 6 = 34 years old, and Lyn was 60 - 6 = 54 years old.