Question 1209934
Let's use variables to represent the daily wages:

* Let 't' represent the daily wage of a technician.
* Let 'a' represent the daily wage of an apprentice.

We can set up two equations based on the given information:

**Equation 1:** 7 technicians and 3 apprentices earn 820.
   * 7t + 3a = 820

**Equation 2:** If one apprentice becomes a technician, there are 8 technicians and 2 apprentices, and they earn 880.
   * 8t + 2a = 880

Now we have a system of two linear equations with two variables. We can solve for 't' and 'a'.

**Solve the System of Equations:**

We can use the substitution or elimination method. Let's use the elimination method.

1.  Multiply Equation 1 by 2 and Equation 2 by 3 to make the 'a' coefficients match:
    * (7t + 3a = 820) * 2  =>  14t + 6a = 1640
    * (8t + 2a = 880) * 3  =>  24t + 6a = 2640

2.  Subtract the first modified equation from the second modified equation to eliminate 'a':
    * (24t + 6a) - (14t + 6a) = 2640 - 1640
    * 10t = 1000

3.  Solve for 't':
    * t = 1000 / 10
    * t = 100

4.  Substitute the value of 't' back into either Equation 1 or Equation 2 to solve for 'a'. Let's use Equation 1:
    * 7(100) + 3a = 820
    * 700 + 3a = 820
    * 3a = 820 - 700
    * 3a = 120

5.  Solve for 'a':
    * a = 120 / 3
    * a = 40

**Answers:**

* The daily wage of a technician (t) is $100.
* The daily wage of an apprentice (a) is $40.