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)![]() ![]() ![]() You can put this solution on YOUR website! Hi, Hope I can help \n" ); document.write( ". \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 \n" ); document.write( ". \n" ); document.write( "We can name the number of 3 cent stamps, \"x\" \n" ); document.write( ". \n" ); document.write( "The number of 8 cent stamps is one less than triple the number of 3 cent stamps = \"3x - 1\" \n" ); document.write( ". \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 \" \n" ); document.write( ". \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 \" \n" ); document.write( ". \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) \n" ); document.write( ". \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) = \n" ); document.write( ". \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 \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \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 \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "We will rearrange the numbers = \n" ); document.write( ". \n" ); document.write( "We will combine like terms \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "Now we need to move (-113) to the right side \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "We can now divide each side by \"72\" to find \"x\"(number of 3 cent stamps) \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \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 \n" ); document.write( ". \n" ); document.write( "Number of 3 cent stamps = \"x\" = \"5\" \n" ); document.write( "Number of 8 cent stamps = \" 3x - 1 \" = \n" ); document.write( "Number of 15 cent stamps = \" 3x - 7 \" = \n" ); document.write( ". \n" ); document.write( "We can check our answers by replacing \"x\" with \"5\" in our equation \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \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 = \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 = \n" ); document.write( ". \n" ); document.write( "Here are the three answers \n" ); document.write( ". \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\" \n" ); document.write( ". \n" ); document.write( "Hope I helped, Levi \n" ); document.write( " |