Question 1205484
<pre>

Most teachers use charts to set up word problems.
Also it is easier to set up word problems using
2 unknowns instead of 1.  With 1 unknown you need
the formula 

ONE PART = WHOLE minus OTHER PART.

But when you use two variables, you let x be one part
and y be the other part.

           |------|---------|--------|
           |dollar|  % as   |        |
           |amount| decimal |interest|           
-----------|------|---------|--------|
  1st part |   x  |   0.11  | 0.11x  |
  2nd part |   y  |   0.13  | 0.13y  |
-----------|------|---------|--------|
   totals  | 19000|#########| 2290   | 


The system of equations comes from the 
dollar amount and the interest columns

{{{system(x+y=19000, 0.11x+0.13y=2290)}}}

Solve the first equation for y

{{{y=19000-x}}}

and substitute in

{{{0.11x+0.13y=2290}}}

{{{0.11x+0.13(19000-x)=2290}}}

Clear of decimals by multiplying by 100,
which involves moving the decimal points
two places right, and annexing two zeros
on the term on the right side:

{{{11x+13(19000-x)=229000}}}

{{{11x + 247000 - 13x = 229000}}}

{{{-2x + 247000 = 229000}}}

{{{-2x = 229000-247000}}}

{{{-2x = -18000}}}

{{{x = 9000}}}

Substitute in 

{{{y=19000-x}}}

{{{y=19000-9000}}}

{{{y=10000}}}

Answer:  $9000 at 11% and $10000 at 13%

Edwin</pre>