##DESCRIPTION
##   hcao tagged and PAID on 2-20-2004
##a system ax+by=m, cx+dy=n is given, a,b,m,c,d,n are integers,
##the values of x and y are integer.
##solve using elimination
## DBsubject(Linear algebra)
## DBchapter(Systems of linear equations)
## DBsection(Systems with 2 variables)
## Date(6/3/2002)
## Institution(Rochester)
## Author(Arnie Pizer)
## MLT(usolelim)
## MLTleader(1)
## Level(2)
## TitleText1('Elementary Linear Algebra')
## AuthorText1('Larson, Edwards, Falvo')
## EditionText1('5')
## Section1('1.2')
## Problem1('')
## TitleText2('Linear Algebra with Applications')
## AuthorText2('Jeffrey Holt')
## EditionText2('1')
## Section2('1.1')
## Problem2('')
## KEYWORDS('system','linear equations')
##ENDDESCRIPTION

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
   "PGstandard.pl",     # Standard macros for PG language
   "MathObjects.pl",
   "PGML.pl",
   "contextCurrency.pl",
   "PGcourse.pl",
);

TEXT(beginproblem());
Context("Currency");
$showPartialCorrectAnswers = 1;
do{$a = Currency(random(5,12,0.1));
do{$b = Currency(random(5,12,0.1));} until ($b!=$a);
$x = random(1,40,1);
$y = random(1,40,1);
$n = $x+$y;
$m = ($a*$x+$b*$y)/$n;
} until ($m == random(1,100,0.1));

BEGIN_PGML

Julia and her husband own a coffee shop. They experimented with mixing a City Roast Columbian coffee that cost [$a] per pound with French Roast Columbian coffee that cost [$b] per pound to make a [$n]-pound blend. Their blend should cost them [$m] per pound. How much of each type of coffee should they buy?

Julia and her husband should mix [________]{$x} pound of the city Roast Columbian coffee, and [________]{$y} pound of the French Roast Columbian coffee  to make [$n]-pound blend.

END_PGML

ENDDOCUMENT();       # This should be the last executable line in the problem.