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November 12th, 2009, 11:13 AM  #1 
Member Joined: Oct 2009 Posts: 39 Thanks: 0  A mixture problem
I know this a mixture problem and I have solved six of these, but this one is not like the others; can someone help please? My old Chevy Malibu loves super premium gas. Unfortunately, my sister drove it one day and topped it off with? (continued) with 5 gallons of regular gas. The tank holds 16 gallons. My car gets 17 miles per gallon. What is the minimum number of miles I will have to drive the car so that when I fill up the gas tank with super premium gas, the mixture in the gas tank will be at least 95% super premium gas? 
November 12th, 2009, 03:29 PM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Re: A mixture problem Hello, alikn! You're right . . . This is trickier than the usual "mixture problem." I'll walk (and talk) you through it. This walk'ntalk approach can be used most mixture problems. Quote:
Let = number of gallons of gas you will use up and replace with Super. [color=beige]. . [/color]We will be concerned with the amount of Super in the tank. The tank starts with a mixture: 11 gallons of Super and 5 gallons of Regular. [color=beige]. . [/color]It contains 68.75% Super. You drive and use up gallons of the mixture. [color=beige]. . [/color]So, gallons of Super is gone. Then you fill the tank with Super. [color=beige]. . [/color]So, gallons of Super is added. Hence, the final amount of Super is:[color=beige] .[/color] gallons. But we know that the final mixture should be at least 95% Super. [color=beige]. . [/color]It should contain at least:[color=beige] .[/color] gallons of Super. And there is our equation![color=beige] . [/color] . . . [color=beige] .[/color] [color=beige]. . [/color]Solve for You must use up at least 13.44 gallons of the mixed gas. At 17 mpg, you must drive at least:[color=beige] .[/color] miles.  
November 14th, 2009, 10:41 PM  #3 
Global Moderator Joined: Dec 2006 Posts: 20,098 Thanks: 1905 
Initially, the mixture is 5/16 regular (5 gallons). To reduce that to 5% of 16 gallons, i.e., 0.8 gallons, requires using 4.2 gallons of regular, which corresponds to 4.2 gallons/(5/16) of mixture, i.e., 13.44 gallons of mixture. If the car gets 17 miles per gallon of the mixture, it therefore needs to be driven 13.44 × 17 miles, i.e., 228.48 miles.

November 16th, 2009, 12:22 PM  #4 
Member Joined: Oct 2009 Posts: 39 Thanks: 0  Re: A mixture problem
Thanks evryone for your help. It is greatly appriciated.


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