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Wed Feb 22 20:38:15 2006 UTC (7 years, 2 months ago) by jjholt
File size: 2916 byte(s)
```Tags as of Feb 22, 2006.
--JH
```

```    1 ## DESCRIPTION
2 ## Systems of Linear Equations
3 ## ENDDESCRIPTION
4
5 ## KEYWORDS('Algebra' 'Linear Equations' 'Matrix' 'Matrices')
6 ## Tagged by tda2d
7
8 ## DBsubject('Algebra')
9 ## DBchapter('Systems of Equations and Inequalities')
10 ## DBsection('Systems of Linear Equations')
11 ## Date('')
12 ## Author('')
13 ## Institution('ASU')
14 ## TitleText1('')
15 ## EditionText1('')
16 ## AuthorText1('')
17 ## Section1('')
18 ## Problem1('')
19
20 DOCUMENT();        # This should be the first executable line in the problem.
21
23 "PGasu.pl",
24 "PG.pl",
25 "PGbasicmacros.pl",
26 "PGchoicemacros.pl",
28 "PGmatrixmacros.pl"
29 );
30
31 TEXT(&beginproblem);
32 \$showPartialCorrectAnswers = 1;
33 \$ENV{'partial_weights'} = [1,1,1,1,1,1,1,1,1,1,1,1,12,12,12];
35
36
37 \$a1 = random(10,50,.5);
38 \$a2 = random(10,50,.5);
39 \$a3 = random(10,50,.5);
40
41 \$x1 = random(10,50,10);
42 \$x2 = random(10,50,10);
43 \$x3 = random(10,50,10);
44
45 \$l = non_zero_random(.5,2,.5);
46 \$m = non_zero_random(10,20,5);
47 \$n = non_zero_random(10,20,5);
48
49 \$y1 = \$x1*\$l;
50 \$y2 = \$x2*\$l+\$m;
51 \$y3 = \$x3*\$l+\$n;
52
53 \$p = non_zero_random(.5,2,.5);
54 \$q = non_zero_random(10,20,10);
55 do {\$r = non_zero_random(10,20,10); } until ((\$m*\$r != \$q*\$n));
56
57 \$z1 = \$x1*\$p;
58 \$z2 = \$x2*\$p+\$q;
59 \$z3 = \$x3*\$p+\$r;
60
61 \$tot1 = \$a1*\$x1+\$a2*\$y1+\$a3*\$z1;
62 \$tot2 = \$a1*\$x2+\$a2*\$y2+\$a3*\$z2;
63 \$tot3 = \$a1*\$x3+\$a2*\$y3+\$a3*\$z3;
64
65
66 BEGIN_TEXT
67 A dietician is planning a meal that supplies certain quantities of vitamin C, calcium, and
68 magnesium.  Three foods will be used, their quantities measured in milligrams.  The
69 nutrients supplied by these foods and the dietary requirements are given in the table below.
70 \$PAR
71 \$BCENTER
72 \{begintable(5)\}
73 \{row( "Nutrient", "Food 1", "Food 2", "Food 3", "Total Required (mg)")\}
74 \{row("Vitamin C", "\(\$x1\)", "\(\$y1\)", "\(\$z1\)", "\(\$tot1\)")\}
75 \{row("Calcium", "\(\$x2\)", "\(\$y2\)", "\(\$z2\)", "\(\$tot2\)")\}
76 \{row("Magnesium", "\(\$x3\)", "\(\$y3\)", "\(\$z3\)", "\(\$tot3\)")\}
77 \{endtable()\}
78 \$ECENTER
79 \$PAR
80 Write the augmented matrix for this problem.
81
82 \$BCENTER
83 \{display_matrix([[ans_rule(10),ans_rule(10),ans_rule(10),ans_rule(10)],
84 [ans_rule(10),ans_rule(10),ans_rule(10),ans_rule(10)],
85 [ans_rule(10),ans_rule(10),ans_rule(10),ans_rule(10)]],
86 'align'=>"ccc|c")
87 \}
88 \$ECENTER
89
90 \$PAR
91 What quantity (mg) of Food 1 is necessary to meet the dietary requirements? \$BR
92 \{ans_rule(10)\} \$PAR
93 What quantity (mg) of Food 2 is necessary to meet the dietary requirements? \$BR
94 \{ans_rule(10)\} \$PAR
95 What quantity (mg) of Food 3 is necessary to meet the dietary requirements? \$BR
96 \{ans_rule(10)\}
97
98 END_TEXT
99
100 ANS(num_cmp(\$x1));
101 ANS(num_cmp(\$y1));
102 ANS(num_cmp(\$z1));
103 ANS(num_cmp(\$tot1));
104 ANS(num_cmp(\$x2));
105 ANS(num_cmp(\$y2));
106 ANS(num_cmp(\$z2));
107 ANS(num_cmp(\$tot2));
108 ANS(num_cmp(\$x3));
109 ANS(num_cmp(\$y3));
110 ANS(num_cmp(\$z3));
111 ANS(num_cmp(\$tot3));
112
113 ANS(num_cmp(\$a1));
114 ANS(num_cmp(\$a2));
115 ANS(num_cmp(\$a3));
116
117
118
119 ENDDOCUMENT();       # This should be the last executable line in the problem.
```

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