document.write( "Question 180229: System of Equations: John is going to Costa Rica over Spring Break. Before his trip, he purchases 10 travelers checks in denominations of $20, $50 and $100, totaling $370. He has twice as many $20 checks as $50 checks. How many of each type of denomination of travelers checks does he have? \n" ); document.write( "
Algebra.Com's Answer #136687 by MathTherapy(10552)\"\" \"About 
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Let the amount of $50 checks be f,
\n" ); document.write( "Then the amount of $20 checks is 2f
\n" ); document.write( "Let the amount of $100 checks be o\r
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\n" ); document.write( "\n" ); document.write( "Therefore, 2f + f + o = 10, or 3f + o = 10
\n" ); document.write( "Then 2f(20) + f(50) + o(100) = 370, or 40f + 50f + o(100) = 370, or 90f + 100o = 370\r
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\n" ); document.write( "\n" ); document.write( " 3f + o = 10 ----------- (i)
\n" ); document.write( " 90f + 100o = 370 --------- (ii)
\n" ); document.write( " -90f - 30o = - 300 -------- (iii) Multiply eq (i) by – 30:
\n" ); document.write( " 70o = 70 Add eq (iii) & eq (ii)
\n" ); document.write( " o = 1
\n" ); document.write( "Substituting 1 for o in eq (i), we get: 3f + 1 = 10
\n" ); document.write( " 3f = 9
\n" ); document.write( " f = 3\r
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\n" ); document.write( "\n" ); document.write( "Therefore, there are 2f, or 2(3) $20 checks, or 6 $20 checks = $120
\n" ); document.write( " There are f or 3 $50 checks = $150
\n" ); document.write( " There is o or 1 $100 check = $100 \r
\n" ); document.write( "\n" ); document.write( "Checking:
\n" ); document.write( "Altogether, there are 6 + 3 + 1 = 10 checks, and these checks add up to $120 + $150 + $100 = $370.
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