To solve this problem, let's assign variables to the ages of Joy and Bob.
Let J be Joy's current age.
Let B be Bob's current age.
According to the problem, Joy is 20 years older than Bob, so we can write the equation:
J = B + 20 --- (Equation 1)
Three years ago, Joy was 5 times as old as Bob, which can be written as:
J - 3 = 5(B - 3) --- (Equation 2)
Now, let's solve this system of equations.
Substitute the value of J from Equation 1 into Equation 2:
(B + 20) - 3 = 5(B - 3)
Simplify the equation:
B + 17 = 5B - 15
Now, let's solve for B:
Subtract B from both sides:
17 = 4B - 15
Add 15 to both sides:
32 = 4B
Divide both sides by 4:
B = 8
Now that we have found Bob's current age, we can substitute this value into Equation 1 to find Joy's age:
J = B + 20
J = 8 + 20
J = 28
Therefore, Bob is currently 8 years old, and Joy is currently 28 years old.