My Math Forum A mixture problem

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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
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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-'n-talk approach can be used most mixture problems.

Quote:
 My old Chevy Malibu loves super premium gas. My sister drove it one day and topped it off 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?

Let $x$ = 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 $x$ gallons of the mixture.
[color=beige]. . [/color]So, $0.6875x$ gallons of Super is gone.

Then you fill the tank with Super.
[color=beige]. . [/color]So, $x$ gallons of Super is added.

Hence, the final amount of Super is:[color=beige] .[/color]$11 \,-\, 0.6875x \,+\, x \:=\:0.3124x \,+\, 11$ 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]$95\% \,\times\, 16 \:=\:15.2$ gallons of Super.

And there is our equation![color=beige] . [/color] . . . [color=beige] .[/color]$0.3125x + 11 \;=\;15.2$

[color=beige]. . [/color]Solve for $x:\;\;x \,=\,13.44$

You must use up at least 13.44 gallons of the mixed gas.

At 17 mpg, you must drive at least:[color=beige] .[/color]$17 \,\times\, 13.44 \:=\: 228.48$ 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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### why is my malibu 2012 filling for than 16gallons

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