document.write( "Question 86748: 6.4\r
\n" ); document.write( "\n" ); document.write( "Part I. Use two variables and two equations to set up each problem. Do not solve.\r
\n" ); document.write( "\n" ); document.write( "1. One integer is twice another and their sum is 96. Find the integers.\r
\n" ); document.write( "\n" ); document.write( "2. The sum of two integers is 38 and their difference is 12. Find the integers.\r
\n" ); document.write( "\n" ); document.write( "3. Three times one integer plus another integer is 29. If the first integer plus twice the
\n" ); document.write( " second is 18, find the integers.\r
\n" ); document.write( "\n" ); document.write( "4. Twice one integer plus another integer is 21. If the first integer plus 3 times the
\n" ); document.write( " second is 33, find the integers.\r
\n" ); document.write( "\n" ); document.write( "Part II. Use two variables and two equations for each problem. Solve the systems by any method you choose, and write the answer in the appropriate form.\r
\n" ); document.write( "\n" ); document.write( "5. A rancher raises five times as many cows as horses. If he has 168 animals, how
\n" ); document.write( " many cows does he have?\r
\n" ); document.write( "\n" ); document.write( "6. A landscaper used 100 pounds of grass seed containing twice as much bluegrass
\n" ); document.write( " as rye. He added 15 more pounds of bluegrass to the mixture before seeding a
\n" ); document.write( " lawn. How many pounds of bluegrass did he use?\r
\n" ); document.write( "\n" ); document.write( "7. A youth group with 26 members is going skiing. Each of the five chaperones will
\n" ); document.write( " drive a van or a sedan. The vans can seat seven people, and the sedans can seat five
\n" ); document.write( " people. How many of each type of vehicle could transport all 31 people to the ski
\n" ); document.write( " area in one trip?\r
\n" ); document.write( "\n" ); document.write( "8. In a mayoral election, the incumbent received 25% more votes than the opponent.
\n" ); document.write( " Altogether, 5175 votes were cast for the two candidates. How many votes did the
\n" ); document.write( " incumbent mayor receive?\r
\n" ); document.write( "\n" ); document.write( "9. The drama club at Lincoln High School sells hot chocolate, and coffee at the
\n" ); document.write( " school’s football games to make money for a special trip. At one game, they sold
\n" ); document.write( " $200 worth of hot drinks. They need to report how many of each type of drink
\n" ); document.write( " they sold for their club records. Macha knows that they used 295 cups that night.
\n" ); document.write( " If hot chocolate sells for $0.75 and coffee sells for $0.50, how many of each type
\n" ); document.write( " of hot drinks did they sell?\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #62770 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Part I. Use two variables and two equations to set \r\n" );
document.write( "up each problem. Do not solve. \r\n" );
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document.write( "You have to learn things like\r\n" );
document.write( "\"Twice\" means \"two times\"\r\n" );
document.write( "\"Sum\" means \"what you get when you add\".\r\n" );
document.write( "\"Is\" means \"equals\".\r\n" );
document.write( "\"Difference\" means \"what you get when you subtract\".\r\n" );
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document.write( "1. One integer is twice another \r\n" );
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document.write( "y = 2x\r\n" );
document.write( "\r\n" );
document.write( "and their sum is 96.  \r\n" );
document.write( "\r\n" );
document.write( "x + y = 96\r\n" );
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document.write( "2. The sum of two integers is 38.  \r\n" );
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document.write( "x + y = 38\r\n" );
document.write( "\r\n" );
document.write( "and their difference is 12.\r\n" );
document.write( "\r\n" );
document.write( "x - y = 12\r\n" );
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document.write( "3. Three times one integer plus another integer is 29.\r\n" );
document.write( "\r\n" );
document.write( "3x + y = 29\r\n" );
document.write( "\r\n" );
document.write( "If the first integer plus twice the\r\n" );
document.write( "second is 18. \r\n" );
document.write( "\r\n" );
document.write( "x + 2y = 18\r\n" );
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document.write( "4. Twice one integer plus another integer is 21.\r\n" );
document.write( "\r\n" );
document.write( "2x + y = 21 \r\n" );
document.write( "\r\n" );
document.write( "If the first integer plus 3 times the \r\n" );
document.write( "second is 33.\r\n" );
document.write( "\r\n" );
document.write( "x + 3y = 33\r\n" );
document.write( "\r\n" );
document.write( "Part II. Use two variables and two equations for \r\n" );
document.write( "each problem. Solve the systems by any method you \r\n" );
document.write( "choose, and write the answer in the appropriate form. \r\n" );
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document.write( "5. A rancher raises five times as many cows as horses.\r\n" );
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document.write( "   C = 5H \r\n" );
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document.write( " If he has 168 animals, \r\n" );
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document.write( "   C + H = 168\r\n" );
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document.write( "Substitute 5H for C in C + H = 165\r\n" );
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document.write( "  5H + H = 168\r\n" );
document.write( "      6H = 168\r\n" );
document.write( "       H = 168/6 = 31 horses\r\n" );
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document.write( "C = 5H = 5(31) = 155 cows.\r\n" );
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document.write( "6. A landscaper used 100 pounds of grass seed \r\n" );
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document.write( "     B + R = 100\r\n" );
document.write( "\r\n" );
document.write( "containing twice as much bluegrass\r\n" );
document.write( "as rye. \r\n" );
document.write( "\r\n" );
document.write( "     B = 2R\r\n" );
document.write( "\r\n" );
document.write( "Substitute 2R for B in B + R = 100\r\n" );
document.write( "\r\n" );
document.write( "    2R + R = 100\r\n" );
document.write( "        3R = 100\r\n" );
document.write( "         R = \"100%2F3\" = 33\"1%2F3\" \r\n" );
document.write( "\r\n" );
document.write( "B = 2R = 2(33\"1%2F3\") = 66\"2%2F3\"\r\n" );
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document.write( "He added 15 more pounds of bluegrass \r\n" );
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document.write( "66\"2%2F3\"+15 = 81\"2%2F3\" pound of bluegrass.\r\n" );
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document.write( "7. A youth group with 26 members is going skiing. \r\n" );
document.write( "Each of the five chaperones will drive a van or \r\n" );
document.write( "a sedan. \r\n" );
document.write( "\r\n" );
document.write( " V +  S =  5\r\n" );
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document.write( "The vans can seat seven people, and the sedans can seat \r\n" );
document.write( "five people. \r\n" );
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document.write( "7V + 5S = 31\r\n" );
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document.write( "Solve the first for S.  S = 5 - V\r\n" );
document.write( "Substitute in 7V + 5S = 31\r\n" );
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document.write( "7V + 5(5 - V) = 31\r\n" );
document.write( " 7V + 25 - 5V = 31\r\n" );
document.write( "      2V + 25 = 31\r\n" );
document.write( "           2V = 31 - 25\r\n" );
document.write( "           2V = 6\r\n" );
document.write( "            V = 6/2 = 3\r\n" );
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document.write( "S = 5 - V = 5 - 3 = 2\r\n" );
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document.write( "2 sedans, 3 vans.  \r\n" );
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document.write( "8. In a mayoral election, the incumbent received \r\n" );
document.write( "25% more votes than the opponent.\r\n" );
document.write( "\r\n" );
document.write( "(\"O\" looks too much like zero, so I'll use the \r\n" );
document.write( "letter \"P\" for \"OPPONENT\")\r\n" );
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document.write( "I = P + .25P\r\n" );
document.write( "or\r\n" );
document.write( "I = 1.00P + .25P\r\n" );
document.write( "or\r\n" );
document.write( "I = 1.25P\r\n" );
document.write( "\r\n" );
document.write( "Altogether, 5175 votes were cast for the two \r\n" );
document.write( "candidates.\r\n" );
document.write( "\r\n" );
document.write( "I + P = 5175\r\n" );
document.write( "\r\n" );
document.write( "Substitute 1.25P for I in I + P = 5175\r\n" );
document.write( "\r\n" );
document.write( "    1.25P + P = 5175\r\n" );
document.write( "1.25P + 1.00P = 5175\r\n" );
document.write( "        2.25P = 5175\r\n" );
document.write( "            P = 5175/2.25\r\n" );
document.write( "            P = 2300\r\n" );
document.write( "\r\n" );
document.write( "I = 1.25P = 1.25(2300) = 2875\r\n" );
document.write( "\r\n" );
document.write( "So the ncumbent mayor received 2875 votes \r\n" );
document.write( "and the opponent received 2300\r\n" );
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document.write( "9. Macha knows that they used 295 cups that night.\r\n" );
document.write( "\r\n" );
document.write( "   H + C = 295\r\n" );
document.write( "\r\n" );
document.write( ">>...hot chocolate sells for $0.75 and coffee sells \r\n" );
document.write( "for $0.50...<<\r\n" );
document.write( "\r\n" );
document.write( ">>...they sold $200 worth of hot drinks...<<\r\n" );
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document.write( " 0.75H + 0.50C = 200\r\n" );
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document.write( "You solve that by yourself!\r\n" );
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document.write( "Answer: H = 210 cups of hot chocolate, C = 85 cups of coffee. \r\n" );
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document.write( "Edwin

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