document.write( "Question 957470: At a concession stand, three hot dogs and two hamburgers cost $7.50; two hot dogs and three hamburgers cost $8.75. Find the cost of one hot dog and one hamburger \n" ); document.write( "

Algebra.Com's Answer #585082 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+a+\"$ = the cost in dollars of 1 hot dog
\n" ); document.write( "Let $\"+b+\"$ = the cost in dollars of 1 hamburger
\n" ); document.write( "------------------------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+3a+%2B+2b+=+7.5+\"$
\n" ); document.write( "(2) $\"+2a+%2B+3b+=+8.75+\"$
\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( "(2) $\"+6a+%2B+9b+=+26.25+\"$
\n" ); document.write( "(1) $\"+-6a+-+4b+=+-15+\"$
\n" ); document.write( "------------------------
\n" ); document.write( " $\"+5b+=+11.25+\"$
\n" ); document.write( " $\"+b+=+2.25+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+3a+%2B+2%2A2.25+=+7.5+\"$
\n" ); document.write( "(1) $\"+3a+=+7.5+-+4.5+\"$
\n" ); document.write( "(1) $\"+3a+=+3+\"$
\n" ); document.write( "(1) $\"+a+=+1+\"$
\n" ); document.write( "1 hot dog costs $1
\n" ); document.write( "1 hamburger costs $2.25
\n" ); document.write( "------------------------
\n" ); document.write( "check:
\n" ); document.write( "(1) $\"+3%2A1+%2B+2%2A2.25+=+7.5+\"$
\n" ); document.write( "(1) $\"+3+%2B+4.5+=+7.5+\"$
\n" ); document.write( "(1) $\"+7.5+=+7.5+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+2%2A1+%2B+3%2A2.25+=+8.75+\"$
\n" ); document.write( "(2) $\"+2+%2B+6.75+=+8.75+\"$
\n" ); document.write( "(2) $\"+8.75+=+8.75+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

\n" );