document.write( "Question 310674: This question was answered but I'm still confused. Can I please have some more help? High school was ten years ago, what little math ability I had is gone.
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document.write( "Thanks Again\r
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document.write( "My question is why is the quanity equation multiplied by 20 and not.2. Also when solving the two equations why does the 20a cancel, but not the 550? I know these are probably very simple, but I just don't understand.\r
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document.write( "How many ml of medication A which has a 20% concentration, and medication B which has a 65% concentration should be mixed to form a 550 ml solution that is 30.9%
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document.write( "Equation:
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document.write( "Quantity Equation:::::::: a + b = 550 ml
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document.write( "Active Ingredient Eq: 0.20a + 0.65b = 0.309*550
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document.write( "Solving using 2 equations and elimination:
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document.write( "Multiply thru the 1st equation by 20
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document.write( "Multiply thru the 2nd equation by 100
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document.write( "20a + 20b = 20*550
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document.write( "20a + 65b = 30.9*550
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document.write( "Subtract 1st from 2nd and solve for \"b\":
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document.write( "45b = 10.9*550
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document.write( "b = 133.22 ml (amt. of 65% solution needed in the mixture)
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document.write( "Since a + b = 550, a = 416.78 ml (amt. of 20% solution needed in the mix) \n" );
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Algebra.Com's Answer #222158 by solver91311(24713)![]() ![]() You can put this solution on YOUR website! \r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Actually, you could multiply the Quantity equation by 2, but then you would have to multiply the Active Ingredient equation by 10 instead of 100.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "As to your other question, let me illustrate it this way. In the first place, I would have used -20 as a multiplier for the Q equation and 100 for the AI equation, thus:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Now, you could multiply out the constant terms in the right-hand sides, and that would actually answer your question about \"why the 550 doesn't cancel\". But let's proceed without that step. Since I used a -20 multiplier for the Q equation, we can actually add the two equations rather than subtracting them. This technique gives you much less chance for a sign error. But rather than just showing the sum of the two, let's use the idea that if \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Now, \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Putting it all back together:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "And finally, as you stated,\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "John \n" ); document.write( " \n" ); document.write( " \n" ); document.write( " |