document.write( "Question 816829: [ If one car costs $14,300 and it gets 35 mpg. And the other car costs [$15,400] and gets 40 mpg. Assuming that gas costs $3.75 per gallon [at what number of driven miles] would the two cars [be of equal value?] ] \n" ); document.write( "
Algebra.Com's Answer #491744 by TimothyLamb(4379)![]() ![]() You can put this solution on YOUR website! 3.75 $/gallon \n" ); document.write( "--- \n" ); document.write( "x = miles driven \n" ); document.write( "--- \n" ); document.write( "car a: \n" ); document.write( "m = 3.75 $/gal * (1/35) gal/mile = 0.1071428 $/mile (fuel cost per mile) \n" ); document.write( "--- \n" ); document.write( "car b: \n" ); document.write( "m = 3.75 $/gal * (1/40) gal/mile = 0.09375 $/mile (fuel cost per mile) \n" ); document.write( "--- \n" ); document.write( "cost of ownership per mile: \n" ); document.write( "--- \n" ); document.write( "a(x) = 0.1071428x + 14300 \n" ); document.write( "b(x) = 0.09375x + 15400 \n" ); document.write( "--- \n" ); document.write( "break even point: \n" ); document.write( "0.1071428x + 14300 = 0.09375x + 15400 \n" ); document.write( "0.1071428x - 0.09375x = 15400 - 14300 \n" ); document.write( "0.0133928x = 1100 \n" ); document.write( "--- \n" ); document.write( "x = 82134 miles \n" ); document.write( "--- \n" ); document.write( "Answer: \n" ); document.write( "the more fuel efficient car-a, which is $1100 more expensive to purchase, will not match the less fuel efficient car-b in terms of operating cost per mile, until the cars have each been driven 82,134 miles. In other words, the more fuel efficient car-a will cost more to operate per mile than car-b, until both cars have each been driven 82,134 miles, at which time car-a will cost less to operate per mile than car-b. \n" ); document.write( "--- \n" ); document.write( "Solve and graph linear equations: \n" ); document.write( "https://sooeet.com/math/linear-equation-solver.php \n" ); document.write( "--- \n" ); document.write( "Solve quadratic equations, quadratic formula: \n" ); document.write( "https://sooeet.com/math/quadratic-formula-solver.php \n" ); document.write( "--- \n" ); document.write( "Convert fractions, decimals, and percents: \n" ); document.write( "https://sooeet.com/math/fraction-decimal-percent.php \n" ); document.write( "--- \n" ); document.write( "Calculate and graph the linear regression of any data set: \n" ); document.write( "https://sooeet.com/math/linear-regression.php \n" ); document.write( " |