Final answer:
To find Seth and Eric's current ages, we can set up two equations using the given information and solve them simultaneously.
Step-by-step explanation:
To solve this problem, let's start by assigning variables to the ages of Seth and Eric. Let Seth's age be represented by 'S' and Eric's age be represented by 'E'. We are given that currently Seth's age is 4/5 the age of Eric:
S = (4/5)E
We are also given that twenty-one years ago Eric was twice as old as Seth:
E - 21 = 2(S - 21)
Now we can solve these equations simultaneously to find their current ages. Let's substitute the value of S from the first equation into the second equation:
E - 21 = 2((4/5)E - 21)
Simplifying the equation, we get:
E - 21 = (8/5)E - 42
Moving all the terms with 'E' to one side, we get:
(8/5)E - E = 42 - 21
Simplifying further, we get:
(3/5)E = 21
To solve for E, we can multiply both sides of the equation by 5/3:
E = (5/3) * 21 = 35
Now that we know Eric's age, we can substitute this value back into the first equation to find Seth's age:
S = (4/5) * 35 = 28
Therefore, Eric is currently 35 years old and Seth is currently 28 years old.