document.write( "Question 934803: A collection of 120 coins worth of $5.52 consists of pennies, nickels, dimes and quarters. There are 8 more nickels than dimes and three times as many pennies as nickels. How many of each type of coin are there?\r
\n" ); document.write( "\n" ); document.write( "What I've tried:
\n" ); document.write( " x+y+z+w=120
\n" ); document.write( " 1x+5y+10z+25w=552
\n" ); document.write( "
\n" ); document.write( " y=z+8
\n" ); document.write( " x=3y
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\n" ); document.write( "3y+z+8+z+w=120 1(3y)+5(z+8)+10z+25w=552
\n" ); document.write( "3y+2z+w=112 3y+5z+40+10z+25w=552
\n" ); document.write( " 3y+5z+10z+25w=512
\n" ); document.write( " 3y+15z+25w=512
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\n" ); document.write( "(-36y-24z-12w)=-1344
\n" ); document.write( "3y+15z+25w=512
\n" ); document.write( "(-33y-9z+13w)=-832 \n" ); document.write( "
Algebra.Com's Answer #567843 by MathTherapy(10552)\"\" \"About 
You can put this solution on YOUR website!
A collection of 120 coins worth of $5.52 consists of pennies, nickels, dimes and quarters. There are 8 more nickels than dimes and three times as many pennies as nickels. How many of each type of coin are there?\r
\n" ); document.write( "\n" ); document.write( "What I've tried:
\n" ); document.write( " x+y+z+w=120
\n" ); document.write( " 1x+5y+10z+25w=552
\n" ); document.write( "
\n" ); document.write( " y=z+8
\n" ); document.write( " x=3y
\n" ); document.write( "
\n" ); document.write( "3y+z+8+z+w=120 1(3y)+5(z+8)+10z+25w=552
\n" ); document.write( "3y+2z+w=112 3y+5z+40+10z+25w=552
\n" ); document.write( " 3y+5z+10z+25w=512
\n" ); document.write( " 3y+15z+25w=512
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "(-36y-24z-12w)=-1344
\n" ); document.write( "3y+15z+25w=512
\n" ); document.write( "(-33y-9z+13w)=-832
\n" ); document.write( "
Due to the fact that it's extremely messy, at times confusing, and doesn't guarantee correct answers,
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document.write( "it's best to avoid creating too many equations with too many variables. Thus, the easiest and best
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document.write( "strategy is to break this down so you only have 2 variables, as follows:\r
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document.write( "Let number of nickels be N
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document.write( "Then number of dimes is: N - 8, and number of pennies is: 3N
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document.write( "Let number of quarters, be Q
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document.write( "                        N + N - 8 + 3N + Q = 120 ------ Equation denoting number of each denomination
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document.write( "                                     5N - 8 + Q = 120
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document.write( "                                          5N + Q = 128 ------- eq (i)\r
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document.write( ".05N + .1(N - 8) + .01(3N) + .25(Q) = 5.52 ------ Equation denoting value of each denomination
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document.write( "        .05N + .1N - .8 + .03N + .25Q = 5.52
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document.write( "                            .18N - .8 + .25Q = 5.52
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document.write( "                                  .18N + .25Q = 6.32 ------- eq (ii)
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document.write( " 
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document.write( "                                     5N  +    Q = 128 -------- eq (i)
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document.write( "                                  .18N + .25Q = 6.32 ------- eq (ii)
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document.write( "                               - 1.25N - .25Q = - 32 ------- Multiplying eq (i) by - .25 ------ eq (iii)
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document.write( "                                          - 1.07N = - 25.68 --- Adding eqs (iii) & (ii)
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document.write( "                N, or number of nickels = \"%28-+25.68%29%2F%28-+1.07%29\" = \"highlight_green%2824%29\"\r
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document.write( "\n" );
document.write( "                                      5(24) + Q = 128 ------- Substituting 24 for N in eq (i)
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document.write( "                                        120 + Q = 128
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document.write( "             Q, or number of quarters = 128 – 120, or \"highlight_green%288%29\"
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document.write( "             Number of dimes: 24 – 8, or \"highlight_green%2816%29\"
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document.write( "             Number of pennies: 3(24), or \"highlight_green%2872%29\"
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document.write( "You can do the check!! 
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document.write( "===================
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document.write( "Send comments, “thank-yous,” and inquiries to “D” at MathMadEzy@aol.com.
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document.write( "Further help is available, online or in-person, for a fee, obviously. \r
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document.write( "For FREE info and answers to questions about the ASVAB exam, the NYS 3 – 8 city/state wide exams,GENERAL
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document.write( "MATH and HOMEWORK QUESTIONS, or MATH QUESTIONS related to the Regents Integrated Algebra, 
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