My Math Forum Algebra Word Problem

 Algebra Pre-Algebra and Basic Algebra Math Forum

 January 20th, 2013, 07:55 PM #1 Newbie   Joined: Jan 2013 Posts: 2 Thanks: 0 Algebra Word Problem This isn't for an assignment, I am just curious to see it finished, possibly explained a little. This is for my own curiosity. Thanks. A salesperson purchased an automobile that was advertised as averaging 27 mi/gal in the city and 38 mi/gal on the highway. A recent sales trip that covered 2276 miles required 68 gallons of gasoline. Assuming that the advertised mileage estimates were correct, how many miles were driven in the city?
 January 20th, 2013, 08:12 PM #2 Senior Member     Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 521 Math Focus: Calculus/ODEs Re: Algebra Word Problem Let C be the number of miles driven in the city and H be the number of miles driven on the highway. We have: $C+H=2276$ $\frac{C}{27}+\frac{H}{38}=68$ Solving both for H and equating, we find: $2276-C=38$$68-\frac{C}{27}$$$ $\frac{11}{27}C=308$ $C=756$
January 20th, 2013, 08:13 PM   #3
Math Team

Joined: Dec 2006
From: Lexington, MA

Posts: 3,267
Thanks: 408

Re: Algebra Word Problem

Hello, apparentlynothing!

Quote:
 A man bought a car that was advertised as averaging 27 mi/gal in the city and 38 mi/gal on the highway. A recent trip that covered 2276 miles required 68 gallons of gasoline. Assuming that the advertised mileage estimates were correct, how many miles were driven in the city?

$\text{Let }x\,=\text{ number of miles driven in the city.}$
$\text{At 27 mpg, this required: }\,\frac{x}{27}\text{ gallons of gasoline.}$

$\text{Let }y\,=\text{ number of miles driven on the highway.}$
$\text{At 38 mpg, this required: }\,\frac{y}{38}\text{ gallons of gasoline}$

$\text{Hence, the total amount of gas was: }\,\frac{x}{27}\,+\,\frac{y}{38}\:=\:68\;\;[1]$

$\text{The total distance was 2276 miles: }\:x\,+\,y \:=\:2276\;\;[2]$

$\begin{array}{cccccc}\text{Multiply [1] by 1026:}=&38x\,+\,27y=&69,768 \\ \\ \\ \text{Multiply [2] by 27:}=&27x \,+\,27y=&61,452 \end{array}=$

$\text{Subtract: }\:11x \:=\:8316 \;\;\;\Rightarrow\;\;\;x \:=\:756$

$\text{Therefore, 756 miles were driven in the city.}$

 January 21st, 2013, 02:17 AM #4 Global Moderator   Joined: Dec 2006 Posts: 21,036 Thanks: 2274 As 68 gallons allow at most 1836 miles to be driven in the city, the extra 440 miles are achieved by using 40 of the gallons for driving on the highway instead of in the city, so that only 28 gallons are used for driving in the city. Hence the number of miles driven in the city is 28*27 = 756.
 January 21st, 2013, 06:14 PM #5 Newbie   Joined: Jan 2013 Posts: 2 Thanks: 0 Re: Algebra Word Problem Thank you both so much!

 Tags algebra, problem, word

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Doc Algebra 5 October 9th, 2013 01:14 PM Hansmatta Algebra 1 October 28th, 2011 01:28 AM Stang2005 Algebra 10 September 2nd, 2011 07:40 AM sssmath Algebra 10 May 14th, 2009 11:35 AM mvanant123 Algebra 3 November 5th, 2008 11:23 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top