Joy is 2/3 as old as Lyn;Six years ago,Joy is 20 less than Lyn's age,How old are they Six years ago?
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
Let's determine the current ages of Joy and Lyn.
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.
To solve this problem, we can use algebraic equations. Let's assign variables to the ages of Joy and Lyn.
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.