document.write( "Question 1208177: Hi
\n" ); document.write( "Mr Thomas spent $1972 on cars and dolls. He bought 3 times as many cars as dolls. Each doll cost $10 more than each car. She paid $476 more for the cars than the dolls. What is the cost of a doll. \n" ); document.write( "

Algebra.Com's Answer #846409 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "He bought 3 times as many cars as dolls:
\n" ); document.write( "let x = # of dolls
\n" ); document.write( "then 3x = # of dolls

\n" ); document.write( "Each doll cost $10 more than each car:
\n" ); document.write( "let y = cost of each car
\n" ); document.write( "then y+10 = cost of each doll

\n" ); document.write( "total cost of the cars: (3x)(y) = 3xy
\n" ); document.write( "total cost of the dolls: (x)(y+10)=xy+10x

\n" ); document.write( "The total cost was $1972; the cost of the cars was $476 more than the cost of the dolls:
\n" ); document.write( " $\"3xy%2B%28xy%2B10x%29=4xy%2B10x=1972\"$
\n" ); document.write( " $\"3xy-%28xy%2B10x%29=2xy-10x=476\"$

\n" ); document.write( "Eliminate the xy term from the two equations:
\n" ); document.write( " $\"4xy%2B10x=1972\"$
\n" ); document.write( " $\"4xy-20x=952\"$
\n" ); document.write( " $\"30x=1020\"$
\n" ); document.write( " $\"x=34\"$

\n" ); document.write( "He bought x=34 dolls and 3x=102 cars

\n" ); document.write( "Substitute x=34 in one of the equations to solve for y:
\n" ); document.write( " $\"2xy-10x=68y-340=476\"$
\n" ); document.write( " $\"68y=816\"$
\n" ); document.write( " $\"y=12\"$

\n" ); document.write( "The cost of each car was y = $12; the cost of each doll was y+10 = $22

\n" ); document.write( "ANSWER: $22

\n" ); document.write( "CHECK:
\n" ); document.write( "cost of 34 dolls and 102 cars: 34($22)+102($12) = $748+$1224 = $1972
\n" ); document.write( "difference between cost of cars and cost of dolls: $1224-$748 = $476

\n" ); document.write( " \n" ); document.write( "

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