Let the number of days he does an acceptable job = x.
then the number of days he does an outstanding job = 10-x

He got $3.33 for each of the x days, which amounted to $3.33x
He got $3 more for each of the 10-x days, or $3.33+$3 or $6.33,
which amounted to $6.33(10-x)


Get the equation from this:

(The money he got for all x days when he did an acceptable job) 

                       PLUS

(The money he got for all 10-x days when he did an outstanding job)

                      EQUALS

                      $42.30

So the equation is

               $3.33x + $6.33(10 - x) = $42.30
                 3.33x + 6.33(10 - x) =  42.30
Drop the zero
on 42.30, making 
it 42.3
                 3.33x + 6.33(10 - x) =  42.3
Distribute
                 3.33x + 63.3 - 6.33x =  42.3
combine x terms                  
                        -3.00x + 63.3 =  42.3
Drop the zeros
on -3.00x, making
it -3x

                           -3x + 63.3 =  42.3 
subtract 63.3 
from both sides:
                                -63.3 = -63.3
                       ----------------------
                           -3x        = -21

Divide both sides by -3

                           -3x          -21
                          -----       = ----
                           -3            -3

Cancel the -3's on the
left and divide on the
right
                             x        =   7            

The number of days he did an acceptable job = x = 7 days
The number of days he did an outstanding job = 10-x = 10-7 = 3 days
 
Edwin