document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=386243>Question 386243</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 400 gram solution is 25% salt. How much salt must be added to produce a solution that is 40% salt? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #273087 by </B><A HREF=/tutors/aboutme.mpl?userid=gwendolyn><B>gwendolyn(128)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gwendolyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=gwendolyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=273087\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First of all, we'll determine our variables:<BR>\n" );
document.write( "let x=grams of salt that you already have<BR>\n" );
document.write( "let y=grams of salt that need to be added<BR>\n" );
document.write( "let z=total amount of salt in the solution after adding salt\r<BR>\n" );
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document.write( "We know that salt makes up 25% of the 400g solution, and that 25% can also be written as .25. Thus, we can write an equation to determine x's value:<BR>\n" );
document.write( "x=.25*400g<BR>\n" );
document.write( "x=100g\r<BR>\n" );
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document.write( "Therefore, there are 100 grams of salt already in the solution.\r<BR>\n" );
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document.write( "Now that we've determined x's value, we'll bring z into the equation. There are two ways to calculate z. z is equivalent to the sum of x and y. Remember, x is equal to 100 grams. So, z's equation is as follows:<BR>\n" );
document.write( "z=100g+y\r<BR>\n" );
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document.write( "The other way to calculate z is as a percentage of the final solution. As the question states, we want the final solution to have a salt content of 40% (which we can write as .40). The final amount of solution can be written as below:<BR>\n" );
document.write( "400g+y=total amount of solution after adding salt.<BR>\n" );
document.write( "This is because we are adding y (the amount of salt needed to bring the salt content to 40 percent)to the amount of solution which we already have. <BR>\n" );
document.write( "Therefore, the second way to express z is below:<BR>\n" );
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document.write( "z=.40*(400g+y)\r<BR>\n" );
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document.write( "After we have two equations for z, we can set them equal to each other as follows:\r<BR>\n" );
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document.write( "100g+y=.40*(400g+y)\r<BR>\n" );
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document.write( "We then can distribute the .40 over the parenthesis.\r<BR>\n" );
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document.write( "100g+y=160g+.40y\r<BR>\n" );
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document.write( "And then we can subtract 100 grams from both sides of the equation.<BR>\n" );
document.write( "y=60g+.40y\r<BR>\n" );
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document.write( "Next, we subtract .40 y from both sides of the equation to get y on one side.<BR>\n" );
document.write( ".6y=60g\r<BR>\n" );
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document.write( "Finally, we can divide both sides by .6 to isolate y.<BR>\n" );
document.write( "y=100g\r<BR>\n" );
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document.write( "Therefore, you must add 100g of salt to the solution to make it 40 percent salt.<BR>\n" );
document.write( " </SPAN>\n" );
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