document.write( "Question 894900: Ali,Ben and charles shared teh cost of a present. The ratio of the amount paid by ali to the total amount paid of Ben adn charles was 2: 3 while Ben's share was 20% o fthe total amount paid by ali and charles. Given that charles paid 84 more then Ben, How much did the present cost.? \n" ); document.write( "

Algebra.Com's Answer #542417 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let the amounts paid by each = a, b, and c
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2F+%28+b+%2B+c+%29+=+2%2F3+\"$
\n" ); document.write( "(2) $\"+b+=+.2%2A%28+a+%2B+c+%29+\"$
\n" ); document.write( "(3) $\"+c+=+b+%2B+84+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "This is 3 equations and 3 unknowns, so it's solvable
\n" ); document.write( "Multiply both sides of (1) by $\"+3%2A%28+b+%2B+c+%29+\"$
\n" ); document.write( "(1) $\"+3a+=+2%2A%28+b+%2B+c+%29+\"$
\n" ); document.write( "(1) $\"+3a+=+2b+%2B+2c+\"$
\n" ); document.write( "and
\n" ); document.write( "(2) $\"+b+=+.2a+%2B+.2c+\"$
\n" ); document.write( "(2) $\"+.2a+=+b+-+.2c+\"$
\n" ); document.write( "(2) $\"+a+=+5b+-+c+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "Substitute (2) into (1)
\n" ); document.write( "(1) $\"+3%2A%28+5b+-+c+%29+=+2b+%2B+2c+\"$
\n" ); document.write( "(1) $\"+15b+-+3c+=+2b+%2B+2c+\"$
\n" ); document.write( "(1) $\"+13b+=+5c+\"$
\n" ); document.write( "(1) $\"+b+=+%28+5%2F13+%29%2Ac+\"$
\n" ); document.write( "----------------------
\n" ); document.write( "Substitute (1) into (3)
\n" ); document.write( "(3) $\"+c+=+b+%2B+84+\"$
\n" ); document.write( "(3) $\"+c+=+%285%2F13%29%2Ac+%2B+84+\"$
\n" ); document.write( "(3) $\"+13c+=+5c+%2B+1092+\"$
\n" ); document.write( "(3) $\"+8c+=+1092+\"$
\n" ); document.write( "(3) $\"+c+=+136.5+\"$
\n" ); document.write( "and
\n" ); document.write( "(3) $\"+c+=+b+%2B+84+\"$
\n" ); document.write( "(3) $\"+b+=+c+-+84+\"$
\n" ); document.write( "(3) $\"+b+=+136.5+-+84+\"$
\n" ); document.write( "(3) $\"+b+=+52.5+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2F+%28+b+%2B+c+%29+=+2%2F3+\"$
\n" ); document.write( "(1) $\"+a+%2F+%28+52.5+%2B+136.5+%29+=+2%2F3+\"$
\n" ); document.write( "(1) $\"+a+%2F+189+=+2%2F3+\"$
\n" ); document.write( "(1) $\"+3a+=+378+\"$
\n" ); document.write( "(1) $\"+a+=+126+\"$
\n" ); document.write( "and
\n" ); document.write( " $\"+a+%2B+b+%2B+c+=+126+%2B+52.5+%2B+136.5+\"$
\n" ); document.write( " $\"+a+%2B+b+%2B+c+=+315+\"$
\n" ); document.write( "The present costs $315
\n" ); document.write( "------------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+b+=+.2%2A%28+a+%2B+c+%29+\"$
\n" ); document.write( "(2) $\"+b+=+.2%2A%28+126+%2B+136.5+%29+\"$
\n" ); document.write( "(2) $\"+b+=+.2%2A262.5+\"$
\n" ); document.write( "(2) $\"+b+=+52.5+\"$
\n" ); document.write( "OK
\n" ); document.write( "Hope I got it!\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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