document.write( "Question 1207292: 360L of paint is made by mixing 3 paints A, B C . the ratio by amount of paint A to B is 3:2 and that of B to C is 1:2 Paint A costs 1800 per liter Paint B costs 2400 per liter and Paint C 1275 per litre . find the amount of each paint , the amount of money needed to make one liter of the mixture \n" ); document.write( "

Algebra.Com's Answer #845078 by ikleyn(52798) $\"\"$ $\"About$

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\n" ); document.write( "360 liters of paint is made by mixing 3 paints A, B and C.
\n" ); document.write( "The ratio by amount of paint A to B is 3:2 and that of B to C is 1:2.
\n" ); document.write( "Paint A costs 1800 per liter. Paint B costs 2400 per liter. Paint C costs 1275 per liter .
\n" ); document.write( "(a) Find the amount of each paint in 360 liters of the mixture.
\n" ); document.write( "(b) Find the amount of money needed to make one liter of the mixture.
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document.write( "To say that    \"The ratio by amount of paint A to B is 3:2 and that of B to C is 1:2\"  is the same\r\n" );
document.write( "as to say that \"The ratio by amount of paint A to B is 3:2 and that of C to B is 2:1\". \r\n" );
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document.write( "Let 2x be the amount of paint B in 360 liters of the mixture.\r\n" );
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document.write( "Then the amount of paint A is   = 3x liters,\r\n" );
document.write( "and the amount of paint C is  2*(2x) = 4x.\r\n" );
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document.write( "So, the 360 liters of the mixture is made of 3 equal parts of A,\r\n" );
document.write( "two equal parts of B and 4 equal parts of C. \r\n" );
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document.write( "Or, in all, 360 liters of the mixture is made of 3+2+4 = 9 equal parts of A, B and C.\r\n" );
document.write( "Thus each elementary part is 360/9 = 40 liters.\r\n" );
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document.write( "Hence, the 360 liters of the mixture paint is made of 3*40 = 120 L of paint A,\r\n" );
document.write( "2*40 = 80 liters of paint B and 4*40 = 160 liters of paint C. \r\n" );
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document.write( "       It completes question (a).\r\n" );
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document.write( "The total cost of 360 liters is then\r\n" );
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document.write( "    120*1800 + 80*2400 + 160*1275 = 512000\r\n" );
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document.write( "and the cost of one liter of the mixture is\r\n" );
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document.write( "    512000/360 = 1700.\r\n" );
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document.write( "       It completes question (b).\r\n" );
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\n" ); document.write( "\n" ); document.write( "I intently presented the solution at the level of arithmetic problem to avoid using equations,
\n" ); document.write( "since this logic and this reasoning is accessible to 4-th grade young students, who just know
\n" ); document.write( "addition, multiplication and division of integer numbers, but may not know equations yet.\r
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