6 YEARS AGO, JOE WAS 2 YEARS MORE THAN 5 TIMES AS OLD AS HIS DAUGHTER. SIX YEAS FROM NOW, HE WILL BE 11 YEARS MORE THAN TWICE AS OLD AS SHE WILL BE. HOW OLD IS JOE?

J - 6 = 5 (D - 6) + 2 ... J - 6 = 5 D - 28

J + 6 = 2(D + 6) + 11 ... J + 6 = 2 D + 23

5 D - 22 = 2 D + 17

solve for D , substitute back to find J

To solve this problem, let's break it down into two equations and solve them simultaneously.

Let's start by defining the variables:
Let J be Joe's age currently,
Let D be his daughter's age currently.

According to the first statement, 6 years ago, Joe was 2 years more than 5 times as old as his daughter:
J - 6 = 5(D - 6) + 2

Simplifying the equation:
J - 6 = 5D - 30 + 2
J - 6 = 5D - 28
J = 5D - 28 + 6
J = 5D - 22 ---- Equation 1

According to the second statement, six years from now, Joe will be 11 years more than twice as old as his daughter will be:
J + 6 = 2(D + 6) + 11

Simplifying the equation:
J + 6 = 2D + 12 + 11
J + 6 = 2D + 23
J = 2D + 23 - 6
J = 2D + 17 ---- Equation 2

Now we have a system of two equations (Equation 1 and Equation 2), which we can solve simultaneously.

To eliminate the variable J, we can subtract Equation 2 from Equation 1:

5D - 22 - (2D + 17) = 0
5D - 2D - 22 - 17 = 0
3D - 39 = 0
3D = 39
D = 39 / 3
D = 13

Now that we know the daughter's age, we can substitute D = 13 into Equation 1 to find Joe's age:

J = 5D - 22
J = 5 * 13 - 22
J = 65 - 22
J = 43

Therefore, Joe is currently 43 years old.