document.write( "Question 1129795: One drink contains 5% fruit juice and another contains 50% fruit juice. How many gallons of each type should be combined to make 5 gallons of a drink that contains 40% fruit juice? (Please solve this using substitution method.) \n" ); document.write( "

Algebra.Com's Answer #746408 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "

\r\n" );
document.write( "Let x be the amount (= the volume) of the 5% fruit juice (in gallons), and\r\n" );
document.write( "let y be the amount (= the volume) of the 50% fruit juice.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Then you have two equations\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "     x +      y =     5     gallons   (1)    (the total volume)\r\n" );
document.write( "0.05*x + 0.50*y = 0.4*5     gallons   (2)    (the volume of the pure juice).\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "The setup is completed.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "To solve the system, I will apply the Substitution method.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "For it, express x = 5-y from the first equation and substitute it into the second equation, replacing x. You will get\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "0.05*(5-y) + 0.5*y = 0.4*5       \r\n" );
document.write( "\r\n" );
document.write( "0.25 - 0.05y + 0.5y = 2,\r\n" );
document.write( "\r\n" );
document.write( "0.45y = 2 - 0.25\r\n" );
document.write( "\r\n" );
document.write( "0.45y = 1.75  ====>  y =  =  =  =  =  =  = .\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Answer.   of the 50% fruit juice and the rest   -  =  gallons of the 5% fruit juice.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Check.  Equation (1):   +  = 5.   ! Correct !\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "        Equation (2):  Left side of the eq. (2) is   +  =  =  = 2 gallons of the pure juice.\r\n" );
document.write( "\r\n" );
document.write( "                       Right side of the eq(2) is  0.4*5 = 2 gallons of the pure juice.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "         Both sides are equal  <-------->  the solution (the answer) is correct !\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "Solved. \r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "---------------------\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "It is a standard and typical mixture problem.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "For introductory lessons covering various types of mixture word problems see\r
\n" ); document.write( "\n" ); document.write( "    - Mixture problems\r
\n" ); document.write( "\n" ); document.write( "    - More Mixture problems\r
\n" ); document.write( "\n" ); document.write( "    - Solving typical word problems on mixtures for solutions \r
\n" ); document.write( "\n" ); document.write( "    - Typical word problems on mixtures from the archive\r
\n" ); document.write( "\n" ); document.write( "in this site.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "You will find there ALL TYPICAL mixture problems with different methods of solutions,
\n" ); document.write( "explained at different levels of detalization, from very detailed to very short.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Read them and become an expert in solution mixture word problems.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook in ALGEBRA-I in this site\r
\n" ); document.write( "\n" ); document.write( "    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "The referred lessons are the part of this textbook in the section \"Word problems\" under the topic \"Mixture problems\".\r
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Save the link to this online textbook together with its description\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Free of charge online textbook in ALGEBRA-I
\n" ); document.write( "https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "to your archive and use it when it is needed.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );