document.write( "Question 1187542: Aling Maria has a candy stall in the market. One candy cost 5 cents each, the second cost 20 cents each and the 3rd cost 30 cents each. In her absence due to personal necessity an honest buyer picked a total of 20 pcs. of candies costing 5 cents, 20 cents and 30 cents in the stall and leave 2 pesos for their exact cost. How many each candy of 5 cents, 20 cents, and 30 cents the honest buyer picked? \n" ); document.write( "

Algebra.Com's Answer #818546 by ikleyn(52784) $\"\"$ $\"About$

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\n" ); document.write( "Aling Maria has a candy stall in the market.
\n" ); document.write( "One candy cost 5 cents each, the second cost 20 cents each and the 3rd cost 30 cents each.
\n" ); document.write( "In her absence due to personal necessity an honest buyer picked a total of
\n" ); document.write( "20 pcs. of candies costing 5 cents, 20 cents and 30 cents in the stall and leave 2 pesos for their exact cost.
\n" ); document.write( "How many each candy of 5 cents, 20 cents, and 30 cents the honest buyer picked?
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document.write( "Let x be the number of 5-cent candies; \r\n" );
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document.write( "    y be the number of 20-cent candies,\r\n" );
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document.write( "and z be the number of 30-cent candies.\r\n" );
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document.write( "As you read the problem, you can write these two equations\r\n" );
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document.write( "     x +   y +   z =  20      (pieces of candies)\r\n" );
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document.write( "    5x + 20y + 30z = 200      (cents, which is 2 pesos)\r\n" );
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document.write( "To simplify, divide all the terms in the second equation by 5.  You will get these two equations\r\n" );
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document.write( "     x +  y +  z = 20         (1)\r\n" );
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document.write( "     x + 4y + 6z = 40         (2)\r\n" );
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document.write( "Now subtract equation (1) from equation (2).  You will get\r\n" );
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document.write( "         3y + 5z = 20.\r\n" );
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document.write( "You should find the solutions to this equation in integer positive numbers, according to the problem's meaning.\r\n" );
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document.write( "Using this additional restrain, you have ONLY ONE unique solution  z = 1,  y = 5  (simply by \"trial and error\" method \r\n" );
document.write( "which is VERY EASY in this case).\r\n" );
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document.write( "Then  from equation (1), you get  x = 20 - 1 - 5 = 14.\r\n" );
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document.write( "ANSWER.  14 5-cent candies;  5 20-cent candies  and  1 30-cent candy.\r\n" );
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document.write( "CHECK.   14*5 + 5*20 + 1*30 = 70 + 100 + 30 = 200 cents = 2 pesos, the total cost.   ! Correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Usually (and as a rule), three unknowns require three equations, in order for the problem had a unique solution.\r
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\n" ); document.write( "\n" ); document.write( "But this problem demonstrates an exclusive case.\r
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\n" ); document.write( "\n" ); document.write( "The problem gives only 2 equations for 3 unknowns, but the additional restrain\r
\n" ); document.write( "\n" ); document.write( "that the solution should be in integer positive numbers provides the UNIQUE answer (!)\r
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\n" ); document.write( "\n" ); document.write( "So, this restrain works as a replacement to third equation (which absents (!) )\r
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