document.write( "Question 250848: You purchase 8 gal of paint and 3 brushes for $152.50. The next day, you purchase 6 gal of paint and 2 brushes for $113.00. How much does each gallon of paint and each brush cost? \n" ); document.write( "

Algebra.Com's Answer #184441 by drk(1908) $\"\"$ $\"About$

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We need to set up 2 equations with two unknowns. Let P = paint and B = brushes.
\n" ); document.write( "(i) $\"8P+%2B+3B+=+152.50\"$
\n" ); document.write( "(ii) $\"6P+%2B+2B+=+113.00\"$
\n" ); document.write( "Now, we have to eliminate a variable. I think multiply (i) by 2 and (ii) by -3 will be easier to do. we get
\n" ); document.write( "(iii) $\"16P+%2B+6B+=+305.00\"$
\n" ); document.write( "(iv) $\"-18P+-6B+=+-339.00\"$
\n" ); document.write( "Add down to eliminate the B. we get
\n" ); document.write( " $\"-2P+=+-34\"$
\n" ); document.write( " $\"+P+=+17\"$
\n" ); document.write( "Now sub this answer back into (i) to get B, which is B = 5.50.
\n" ); document.write( "each gallon of paint is $17, and each paint brush is $5.50.
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