document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=206742>Question 206742</A>: <I><SPAN STYLE=\"word-break: break-all;\"> John and Charles buy red and blue certificates. John buys 10 red and 20 blue and pays $40. Charles buys 10 blue and 20 red and pays $50. The following day, they find out that they need more certificates and they go together to buy 3 red and 2 blue. How much did they pay for these five certificates?\r<BR>\n" );
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document.write( "(A) $5 (B) $6 (C) $7 (D) $8 (E) $9 </SPAN>\n" );
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document.write( "Before you solve this, you have to know the price for one blue and red certificate.<BR>\n" );
document.write( " Let red and blue certificate be x and y respectively. <BR>\n" );
document.write( "John buys 10 red and 20 blue and pays $40. This can be expressed as 10x + 20y = 40<BR>\n" );
document.write( "Charles buys 10 blue and 20 red and pays $50. this is also 20x + 10y = 50<BR>\n" );
document.write( "10x + 20y = 40 ------- Eqn 1<BR>\n" );
document.write( "20x + 10y = 50 ------- Eqn 2<BR>\n" );
document.write( "Multiply Eqn 1 by 2<BR>\n" );
document.write( "20x + 40y = 80 ------- Eqn 1<BR>\n" );
document.write( "20x + 10y = 50 ------- Eqn 2<BR>\n" );
document.write( "Eqn. 1 - Eqn. 2 <BR>\n" );
document.write( "30y = 30<BR>\n" );
document.write( "Divide both side by 30<BR>\n" );
document.write( "y = 1<BR>\n" );
document.write( "Put y = 1 into eqn. 1<BR>\n" );
document.write( "10x + 20(1)= 40<BR>\n" );
document.write( "10x + 20 = 40<BR>\n" );
document.write( "10x = 40 - 20<BR>\n" );
document.write( "10x = 20<BR>\n" );
document.write( "Divide both side by 10<BR>\n" );
document.write( "So we have x = 2<BR>\n" );
document.write( "Hence, x = 2 and y = 1<BR>\n" );
document.write( "So one red certificate cost $ 2 and one blue certificate cost $ 1<BR>\n" );
document.write( "So the cost for 3 red certificates is 2 x 3 = $ 6<BR>\n" );
document.write( "And the cost of 2 red certificates is 1 x 2 = $ 2<BR>\n" );
document.write( "Total will be $ 6 + $ 2 = $ 8<BR>\n" );
document.write( "Hence, they pay $ 8 for these five certificates. </SPAN>\n" );
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