Question 1036234
<pre>
Let the number of hits be x
Let the number of misses be y

                      Value      Value
Type       Number       of         of
 of          of        EACH       ALL
shot        shots      shot      shots
-------------------------------------------
hits         x       $0.07       $0.07x
misses       y      -$0.05      -$0.05y
-------------------------------------------
TOTALS      29       -----      -$0.37

 The first equation comes from the "Number of shots" column.

  {{{(matrix(3,1,Number,of,hits))}}}{{{""+""}}}{{{(matrix(3,1,Number,of,misses))}}}{{{""=""}}}{{{(matrix(4,1,total,number,of,shots))}}}

                     x + y = 29

 The second equation comes from the "Value of all shots" column.
  {{{(matrix(4,1,Value,of,ALL,hits))}}}{{{""+""}}}{{{(matrix(4,1,Value,of,ALL,misses))}}}{{{""=""}}}{{{(matrix(5,1,Total,value,of,ALL,shots))}}}

            0.07x - 0.05y = -0.37

Get rid of decimals by multiplying every term by 100:

                 7x + -5y = -37

 So we have the system of equations:

           {{{system(x + y = 29,7x + -5y = -37)}}}.

We solve by substitution.  Solve the first equation for y:

                                x + y = 29
                                    y = 29 - x

Substitute (29 - x) for y in 7x + -5y = -37

                       7x - 5(29 - x) = -37
                        7x - 145 + 5x = -37
                           12x + -145 = -37
                                  12x = 108
                                    x = 9 = the number of hits.

                      Substitute in y = 29 - x
                                    y = 29 - (9)
                                    y = 20 misses.

Checking:  9 hits is $0.63 and 20 miss is -$1.00
            That's 29 shots.
            And indeed $0.63 - $1.00 = -$0.37

Edwin</pre>