document.write( "Question 100245This question is from textbook
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document.write( ": you fill your car's gas tank when it is about 1/2 empty. The next week, you fill the tank a second time when it is about 3/4 empty. If you buy a total of 18 1/2 gallons of gas on these two days, about how many gallons does the tank hold? \n" );
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Algebra.Com's Answer #73001 by bucky(2189)![]() ![]() ![]() You can put this solution on YOUR website! Let x be the capacity of the tank. \n" ); document.write( ". \n" ); document.write( "The first time you fill it up you pump in 1/2 of x which in decimal form is 0.5x. The next time \n" ); document.write( "you fill it up you pump in 3/4 of x which in decimal form is 0.75x. Together these two fill-ups \n" ); document.write( "total 18 & 1/2 gallons or in decimal form 18.5 gallons. Write this in equation \n" ); document.write( "form: \n" ); document.write( ". \n" ); document.write( "0.5x + 0.75x = 18.5 \n" ); document.write( ". \n" ); document.write( "Add the two terms on the left side and the equation becomes: \n" ); document.write( ". \n" ); document.write( "1.25x = 18.5 \n" ); document.write( ". \n" ); document.write( "Solve for x by dividing both sides of this equation by 1.25 to get: \n" ); document.write( ". \n" ); document.write( "x = 18.5/1.25 = 14.8 gallons \n" ); document.write( ". \n" ); document.write( "So the tank holds about 14.8 gallons when full. \n" ); document.write( ". \n" ); document.write( "The only reason I converted to decimal form was to avoid working with fractions. You could \n" ); document.write( "have just as well done this problem by working it in fraction form, starting with the \n" ); document.write( "equation: \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( ". \n" ); document.write( "where \n" ); document.write( ". \n" ); document.write( "You could now get rid of the denominators by multiplying both sides of this equation (all \n" ); document.write( "terms) by 4 to convert the equation to: \n" ); document.write( ". \n" ); document.write( "2x + 3x = 74 \n" ); document.write( ". \n" ); document.write( "Adding the two terms on the left side results in: \n" ); document.write( ". \n" ); document.write( "5x = 74 \n" ); document.write( ". \n" ); document.write( "and dividing both sides by 5 gives you the answer: \n" ); document.write( ". \n" ); document.write( "x = 14 4/5 \n" ); document.write( ". \n" ); document.write( "and since 4/5 is equivalent to 8/10, this answer is also 14.8 gallons. \n" ); document.write( ". \n" ); document.write( "Hope this helps you to understand the problem a little better. \n" ); document.write( ". \n" ); document.write( " \n" ); document.write( " |