document.write( "Question 1022023: Jen Butler has been pricing speed-pass train fares for a group trip to New York. Three adults and four children must pay $108. Two adults and three children must pay $76. Find the price of the adults ticket and the price of a child's ticket. \n" ); document.write( "

Algebra.Com's Answer #637693 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = the price of an adult's ticket
\n" ); document.write( "Let $\"+b+\"$ = the price of a child's ticket
\n" ); document.write( "----------------------------------
\n" ); document.write( "(1) $\"+3a+%2B+4b+=+108+\"$
\n" ); document.write( "(2) $\"+2a+%2B+3b+=+76+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "Multiply both sides of (1) by $\"+2+\"$
\n" ); document.write( "Multiply both sides of (2) by $\"+3+\"$
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "------------------------------
\n" ); document.write( "(2) $\"+6a+%2B+9b+=+228+\"$
\n" ); document.write( "(1) $\"+-6a+-+8b+=+-216+\"$
\n" ); document.write( "----------------------
\n" ); document.write( " $\"+b+=+12+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+3a+%2B+4b+=+108+\"$
\n" ); document.write( "(1) $\"+3a+%2B+4%2A12+=+108+\"$
\n" ); document.write( "(1) $\"+3a+%2B+48+=+108+\"$
\n" ); document.write( "(1) $\"+3a+=+60+\"$
\n" ); document.write( "(1) $\"+a+=+20+\"$
\n" ); document.write( "---------------
\n" ); document.write( "The price of an adult's ticket is $20
\n" ); document.write( "The price of a child's ticket is $12
\n" ); document.write( "----------------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+2a+%2B+3b+=+76+\"$
\n" ); document.write( "(2) $\"+2%2A20+%2B+3%2A12+=+76+\"$
\n" ); document.write( "(2) $\"+40+%2B+36+=+76+\"$
\n" ); document.write( "(2) $\"+76+=+76+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );