document.write( "Question 1155750: A​ sparkling-water distributor wants to make up 400 gal of sparkling water to sell for $ 8.00 per gallon. She wishes to mix three grades of water selling for ​$14​.00, ​$3​.00, and​ $4.50 per​ gallon, respectively. She must use twice as much of the​ $4.50 water as the $ 3.00 comma water. How many gallons of each should she​ use? \n" ); document.write( "
Algebra.Com's Answer #778408 by josmiceli(19441)\"\" \"About 
You can put this solution on YOUR website!
Let \"+a+\" = gallons of $14 water
\n" ); document.write( "Let \"+b+\" = gallons of $3 water
\n" ); document.write( "Let \"+c+\" = gallons of $4.50 water
\n" ); document.write( "-------------------------------------------
\n" ); document.write( "(1) \"+a+%2B+b+%2B+c+=+400+\"
\n" ); document.write( "(2) \"+%28+14a+%2B+3b+%2B+4.5c+%29+%2F+400+=+8+\"
\n" ); document.write( "(3) \"+c+=+2b+\"
\n" ); document.write( "----------------------
\n" ); document.write( "(2) \"+14a+%2B+3b+%2B+4.5c+=+3200+\"
\n" ); document.write( "(2) \"+28a+%2B+6b+%2B+9c+=+6400+\"
\n" ); document.write( "Multiply both sides of (1) by \"+6+\" and subtract (1) from (2)
\n" ); document.write( "(2) \"+28a+%2B+6b+%2B+9c+=+6400+\"
\n" ); document.write( "(1) \"+-6a+-+6b+-6c+=+-2400+\"
\n" ); document.write( "------------------------------------
\n" ); document.write( "(4) \"+22a+%2B+3c+=+4000+\"
\n" ); document.write( "Plug (3) into (1)
\n" ); document.write( "(1) \"+a+%2B+c%2F2+%2B+c+=+400+\"
\n" ); document.write( "(1) \"+a+%2B+%283%2F2%29%2Ac+=+400+\"
\n" ); document.write( "(1) \"+2a+%2B+3c+=+800+\"
\n" ); document.write( "Subtract (1) from (4)
\n" ); document.write( "(4) \"+22a+%2B+3c+=+4000+\"
\n" ); document.write( "(1) \"+-2a+-+3c+=+-800+\"
\n" ); document.write( "------------------------------
\n" ); document.write( "\"+20a+=+3200+\"
\n" ); document.write( "\"+a+=+160+\"
\n" ); document.write( "and
\n" ); document.write( "(1) \"+a+%2B+b+%2B+c+=+400+\"
\n" ); document.write( "(1) \"+160+%2B+b+%2B+c+=+400+\"
\n" ); document.write( "(1) \"+b+%2B+c+=+240+\"
\n" ); document.write( "Plug (3) into (1)
\n" ); document.write( "(1) \"+b+%2B+2b+=+240+\"
\n" ); document.write( "(1) \"+3b+=+240+\"
\n" ); document.write( "(1) \"+b+=+80+\"
\n" ); document.write( "and
\n" ); document.write( "(1) \"+a+%2B+b+%2B+c+=+400+\"
\n" ); document.write( "(1) \"+160+%2B+80+%2B+c+=+400+\"
\n" ); document.write( "(1) \"+c+=+160+\"
\n" ); document.write( "------------------------------
\n" ); document.write( "160 gallons of $14 water
\n" ); document.write( "80 gallons of $3 water
\n" ); document.write( "160 gallons of $4.50 water
\n" ); document.write( "-------------------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) \"+%28+14a+%2B+3b+%2B+4.5c+%29+%2F+400+=+8+\"
\n" ); document.write( "(2) \"+%28+14%2A160+%2B+3%2A80+%2B+4.5%2A160+%29+%2F+400+=+8+\"
\n" ); document.write( "(2) \"+%28+2240+%2B+240+%2B+720+%29+%2F+400+=+8+\"
\n" ); document.write( "(2) \"+3200+%2F+400+=+8+\"
\n" ); document.write( "(2) \"+3200+=+3200+\"
\n" ); document.write( "OK
\n" ); document.write( "check the math & get a 2nd opinion if needed\r
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