document.write( "Question 1038941: At the Cafe, a lunch of iced tea, a veggie burger, and fries costs $7.56, with the fries costing twice as much as the iced tea. Next week at the Cafe, the price of the iced tea will increase 10% and the price of the veggie burger will increase 25%. After the increase, the same lunch purchase will cost $8.68. Find the price of each item before the increase (round to the nearest penny). \n" ); document.write( "

Algebra.Com's Answer #653739 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = the cost of iced tea the 1st week
\n" ); document.write( "Let $\"+b+\"$ = the cost of a veggie burger the 1st week
\n" ); document.write( "Let $\"+c+\"$ = the cost of the fries the 1st week
\n" ); document.write( "----------------------------------------------
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+756+\"$ ( in cents )
\n" ); document.write( "(2) $\"+c+=+2a+\"$ ( in cents )
\n" ); document.write( "(3) $\"+1.1a+%2B+1.25b+%2B+c+=+868+\"$ ( in cents )
\n" ); document.write( "--------------------------------------
\n" ); document.write( "Multiply both sides of (3) by $\"+100+\"$
\n" ); document.write( "(3) $\"+110a+%2B+125b+%2B+100c+=+86800+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+100+\"$
\n" ); document.write( "and subtract () from (2)
\n" ); document.write( "(3) $\"+110a+%2B+125b+%2B+100c+=+86800+\"$
\n" ); document.write( "(1) $\"+-100a+-+100b+-+100c+=+-75600+\"$
\n" ); document.write( "------------------------------------
\n" ); document.write( "(4) $\"+10a+%2B+25b+=+11200+\"$
\n" ); document.write( "Substitute (2) into (1)
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+2a+=+756+\"$
\n" ); document.write( "(1) $\"+3a+%2B+b+=+756+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+25+\"$ and
\n" ); document.write( "subtract (4) from (1)
\n" ); document.write( "(1) $\"+75a+%2B+25b+=+18900+\"$
\n" ); document.write( "(4) $\"+-10a+-+25b+=+-+11200+\"$
\n" ); document.write( "----------------------------
\n" ); document.write( " $\"+65a+=+7700+\"$
\n" ); document.write( " $\"+a+=+118.46+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+c+=+2a+\"$
\n" ); document.write( "(2) $\"+c+=+236.92+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+3a+%2B+b+=+756+\"$
\n" ); document.write( "(1) $\"+3%2A118.46+%2B+b+=+756+\"$
\n" ); document.write( "(1) $\"+355.38+%2B+b+=+756+\"$
\n" ); document.write( "(1) $\"+b+=+400.62+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "Convert to dollars since answers are in cents:
\n" ); document.write( " $\"+a+=+1.18+\"$
\n" ); document.write( " $\"+b+=+4.01+\"$
\n" ); document.write( " $\"+c+=+2.37+\"$
\n" ); document.write( "The cost of iced tea the 1st week was $1.18
\n" ); document.write( "The cost of a veggie burger the 1st week was $4.01
\n" ); document.write( "The cost of the fries the 1st week was $2.37
\n" ); document.write( "------------------
\n" ); document.write( "check the answers:
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+7.56+\"$ ( in dollars )
\n" ); document.write( "(1) $\"+1.18+%2B+4.01+%2B+2.37+=+7.56+\"$
\n" ); document.write( "(1) $\"+7.56+=+7.56+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+c+=+2a+\"$
\n" ); document.write( "(2) $\"+2.37+=+2%2A1.18+\"$
\n" ); document.write( "(2) $\"+2.37+=+2.36+\"$
\n" ); document.write( "close enough
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+1.1a+%2B+1.25b+%2B+c+=+8.68+\"$ ( in dollars )
\n" ); document.write( "(3) $\"+1.1%2A1.18+%2B+1.25%2A4.01+%2B+2.37+=+8.68+\"$
\n" ); document.write( "(3) $\"+1.298+%2B+5.0125+%2B+2.37+=+8.68+\"$
\n" ); document.write( "(3) $\"+8.6805+=+8.68+\"$
\n" ); document.write( "OK when rounded off \n" ); document.write( "

\n" );