document.write( "Question 156349: A stamp collection consist of 3, 8 and 15 cent stamps. The number of 8 cent stamps is one less than triple the number of 3 cent stamps. The number of 15 cent stamps is six less than the number of 8 cent stamps. The total value of all the stamps is $2.47. Find the number of 8 cent stamps in the collection. \n" ); document.write( "
Algebra.Com's Answer #115157 by Electrified_Levi(103)\"\" \"About 
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Hi, Hope I can help
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\n" ); document.write( "First we have to assign variables for each stamp,(since the 8 cent, and 15 cent stamps rely on the 3 cent stamps [ The number of 8 cent stamps is one less than triple the number of \"3 cent\" stamps.] The number of the 15 cent stamps rely on the 8 cent stamps, which in turn rely on the 3 cent stamps
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\n" ); document.write( "We can name the number of 3 cent stamps, \"x\"
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\n" ); document.write( "The number of 8 cent stamps is one less than triple the number of 3 cent stamps = \"3x - 1\"
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\n" ); document.write( "The number of 15 cent stamps is six less than the number of 8 cent stamps. = \"(3x-1) - 6 \", \" 3x - 1 - 6 \", or \" 3x - 7 \"
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\n" ); document.write( "Number of 3 cent stamps = \"x\"
\n" ); document.write( "Number of 8 cent stamps = \" 3x - 1 \"
\n" ); document.write( "Number of 15 cent stamps = \" 3x - 7 \"
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\n" ); document.write( "Since all the numbers of stamps add up to a value of $2.47, or 247 cents ( we will change the dollars to cents, so we don't have to use a decimal point in our equation)
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\n" ); document.write( "Since it has told us the total value of the stamps, we have to add the stamp value multiplied by the number of stamps( example 3(value)(x)(number of stamps) = \"+3%28x%29+\")
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\n" ); document.write( "we need to add the stamp value multiplied by the number of stamps, add all three stamps(3 cent stamps, 8 cent stamps, 15 cent stamps) together, which add up to 247 cents, here is the equation
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\n" ); document.write( "\"+3%28x%29+%2B+8%283x+-+1%29+%2B+15%283x+-+7%29+=+247+\"
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\n" ); document.write( "Now all we need to do is solve for \"x\", first, we get rid of the parentheses, and use the distribution method
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\n" ); document.write( "\"+3%28x%29+%2B+8%283x+-+1%29+%2B+15%283x+-+7%29+=+247+\" = \"+3x+%2B+24x+-+8+%2B+45x+-+105+=+247+\"
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\n" ); document.write( "We will rearrange the numbers = \"+3x+%2B+24x+%2B+45x+-+8+-+105+=+247+\"
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\n" ); document.write( "We will combine like terms
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\n" ); document.write( "\"+3x+%2B+24x+%2B+45x+-+8+-+105+=+247+\" = [(3x + 24x + 45x)(- 8 - 105) = 247] = \"+72x+-+113+=+247+\"
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\n" ); document.write( "Now we need to move (-113) to the right side
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\n" ); document.write( "\"+72x+-+113+=+247+\" = \"+72x+-+113+%2B+113+=+247+%2B+113+\" = \"+72x+=+360+\"
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\n" ); document.write( "We can now divide each side by \"72\" to find \"x\"(number of 3 cent stamps)
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\n" ); document.write( "\"+72x+=+360+\" = \"+%2872x%2F72%29+=+%28360%2F72%29+\" = \"+x+=+360%2F72+\" = \"+x+=+5+\"
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\n" ); document.write( "\"x\" = 5, here are the numbers of each stamp, in variable form, we can now find how many of each kind of stamp the collection had, ( We found that \"x\" is 5, just replace \"x\" with \"5\" in each equation
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\n" ); document.write( "Number of 3 cent stamps = \"x\" = \"5\"
\n" ); document.write( "Number of 8 cent stamps = \" 3x - 1 \" = \"+3%285%29+-+1+\" = \"+15+-+1+\" = \"14\"
\n" ); document.write( "Number of 15 cent stamps = \" 3x - 7 \" = \"+3%285%29+-+7+\" = \"+15+-+7+\" = \"8\"
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\n" ); document.write( "We can check our answers by replacing \"x\" with \"5\" in our equation
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\n" ); document.write( "\"+3%28x%29+%2B+8%283x+-+1%29+%2B+15%283x+-+7%29+=+247+\" = \"+3%285%29+%2B+8%283%285%29+-+1%29+%2B+15%283%285%29+-+7%29+=+247+\"
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\n" ); document.write( "\"+3%285%29+%2B+8%283%285%29+-+1%29+%2B+15%283%285%29+-+7%29+=+247+\" = \"+15+%2B+%288%29%2815+-+1%29+%2B+%2815%29%2815+-+7%29+=+247+\"
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\n" ); document.write( "\"+15+%2B+%288%29%2815+-+1%29+%2B+%2815%29%2815+-+7%29+=+247+\" = \"+15+%2B+8%2814%29+%2B+15%288%29+=+247+\"
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\n" ); document.write( "\"+15+%2B+8%2814%29+%2B+15%288%29+=+247+\" = \"+15+%2B+112+%2B+120+=+247+\"
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\n" ); document.write( "\"+15+%2B+112+%2B+120+=+247+\" = \"+247+=+247+\" (True)
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\n" ); document.write( "Number of 3 cent stamps = \"5\"
\n" ); document.write( "Number of 8 cent stamps = \"14\" ( The number of 8 cent stamps is one less than triple the number of 3 cent stamps = \"+3%285%29+-+1+\" = \"+15+-+1+=+14+\") (True)
\n" ); document.write( "Number of 15 cent stamps = \"8\" ( The number of 15 cent stamps is six less than the number of 8 cent stamps = \"+14+-+6+=+8+\") (True)
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\n" ); document.write( "Here are the three answers
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\n" ); document.write( "Number of 3 cent stamps = \"5\"
\n" ); document.write( "Number of 8 cent stamps = \"14\"
\n" ); document.write( "Number of 15 cent stamps = \"8\"
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\n" ); document.write( "Hope I helped, Levi
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