Question 1016325
A piggy bank contains $17.35 in nickels, dimes and quarters.
<pre>
$0.05N + $0.10D + $0.25Q = $17.35

Erase $'s and multiply by 100

5N + 10D + 25Q = 1735

Divide through by 5

N + 2D + 5Q = 347
</pre>
The bank contains 3 more quarters than nickels 
<pre>
Q = N + 3
</pre>
and twice as many dimes as quarters. 
<pre>
D = 2Q

{{{system(N + 2D + 5Q = 347,Q=N+3,D=2Q)}}}

{{{system(N + 2D + 5Q = 347,-N+Q=3,D-2Q=0)}}}

{{{system(matrix(3,8,

 N,""+"",2D,""+"",5Q,"",""="",347,
-N,"",   "",""+"", Q,"",""="",3,
 "",""  ,D,""-"",2Q,"",""="",0))}}}

Add the first two equations to eliminate N's

{{{system(matrix(2,8,

 "","",  2D,""+"",6Q,"",""="",350,

 "",""  ,D,""-"",2Q,"",""="",0))}}} 

Divide the first equation through by -2

{{{system(matrix(2,8,

 "","",  -D,""-"",3Q,"",""="",-175,

 "",""  ,D,""-"",2Q,"",""="",0))}}}

Add the equations:

{{{matrix(1,8,

 "","",  "","",-5Q,"",""="",-175)}}}

{{{matrix(1,8,

 "","",  "","",Q,"",""="",35)}}}

Edwin</pre>