four years agoslyvia was two thirds as old as alex was then. four years from now, she will be four fifths as old as alex will be. how old are sylvia and alex now?

Let S be SylVia's current age. Let A be Alex's current age. You have two equations to be solved simultaneously.
S-4 = (2/3)(A-4)
S+4 = (4/5)(A+4)

Subtract the fist equation from the second to eliminate s as a variable.
8 = (2/15)A + 16/5 + 8/3 = (2/15)A + 88/15
Continue the solution yourself

To continue solving the equation, we can simplify it and find the value of A.

8 = (2/15)A + 88/15

First, let's eliminate the fraction by multiplying both sides of the equation by 15:

15 * 8 = 15 * (2/15)A + 15 * (88/15)

120 = 2A + 88

Now, let's isolate the variable A by subtracting 88 from both sides of the equation:

120 - 88 = 2A + 88 - 88

32 = 2A

To find the value of A, divide both sides of the equation by 2:

32/2 = 2A/2

16 = A

Now that we have found the value of A (Alex's current age), we can substitute it back into one of the original equations to solve for S (Sylvia's current age).

Using the first equation:

S - 4 = (2/3)(A - 4)

Substitute A = 16:

S - 4 = (2/3)(16 - 4)

S - 4 = (2/3)(12)

S - 4 = 8

Add 4 to both sides of the equation:

S - 4 + 4 = 8 + 4

S = 12

Therefore, Sylvia is currently 12 years old and Alex is currently 16 years old.