document.write( "Question 630165: a student bought 23 cent, 41 cent, and 80 cent stamps with a total value of $31.50. if the number 23 cent stamps is 2 more that the number of 41 cents stamps, and number of 80 cent stamps is 5 more than one half the number of 41 cents stamps, how many stamps of each denomination did the student obtain? \n" ); document.write( "
Algebra.Com's Answer #396756 by josmiceli(19441)\"\" \"About 
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Let \"+a+\" = the number of 23 cent stamps
\n" ); document.write( "Let \"+b+\" = the number of 41 cent stamps
\n" ); document.write( "Let \"+c+\" = the number of 80 cent stamps
\n" ); document.write( "given:
\n" ); document.write( "(1) \"+23a+%2B+41b+%2B+80c+=+3150+\" ( in cents )
\n" ); document.write( "(2) \"+a+=+b+%2B+2+\"
\n" ); document.write( "(3) \"+c+=+b%2F2+%2B+5+\"
\n" ); document.write( "-----------------
\n" ); document.write( "Substitute (2) and (3) into (1)
\n" ); document.write( "(1) \"+23%2A%28+b+%2B+2+%29+%2B+41b+%2B+80%2A%28+b%2F2+%2B+5+%29+=+3150+\"
\n" ); document.write( "(1) \"+23b+%2B+46+%2B+41b+%2B+40b+%2B+400+=+3150+\"
\n" ); document.write( "(1) \"+23b+%2B+41b+%2B+40b+=+3150+-+46+-+400+\"
\n" ); document.write( "(1) \"+104b+=+2704+\"
\n" ); document.write( "(1) \"+b+=+26+\"
\n" ); document.write( "and, since
\n" ); document.write( "(2) \"+a+=+b+%2B+2+\"
\n" ); document.write( "(2) \"+a+=+26+%2B+2+\"
\n" ); document.write( "(2) \"+a+=+28+\"
\n" ); document.write( "and
\n" ); document.write( "(3) \"+c+=+b%2F2+%2B+5+\"
\n" ); document.write( "(3) \"+c+=+26%2F2+%2B+5+\"
\n" ); document.write( "(3) \"+c+=+13+%2B+5+\"
\n" ); document.write( "(3) \"+c+=+18+\"
\n" ); document.write( "There were 28 of the 23 cent stamps
\n" ); document.write( "There were 26 of the 41 cent stamps
\n" ); document.write( "There were 18 of the 80 cent stamps
\n" ); document.write( "check:
\n" ); document.write( "(1) \"+23a+%2B+41b+%2B+80c+=+3150+\"
\n" ); document.write( "(1) \"+23%2A28+%2B+41%2A26+%2B+80%2A18+=+3150+\"
\n" ); document.write( "(1) \"+644+%2B+1066+%2B+1440+=+3150+\"
\n" ); document.write( "(1) \"+3150+=+3150+\"
\n" ); document.write( "OK
\n" ); document.write( "
\n" );