Category: Science > Math
Asked by: fredewq-ga
List Price: $10.00
04 Dec 2002 16:31 PST
Expires: 03 Jan 2003 16:31 PST
Question ID: 119401
The cost(in$) to buy a given amount of gas(in gallons) plus a wash for a Dodge Durango XLT is given by the following table. Gas(Gallons) Cost($)-includes wash 5 14.7 10 22.65 15 30.60 20 38.55 25 46.50 12.5 27.5 a)Find the model c(x),which gives the total cost(in$)to buy x gallons of gas and a wash. Remember Units! b)Find the derivative model. Remember Units! c)Use the model from part a) to complete the table. d)From the model what is the price per gallon of the gas? e)How much does the wash cost, by itself?
Re: Math Problem
Answered By: blinkwilliams-ga on 04 Dec 2002 20:14 PST
Hi and thanks for the question. a) The model that gives the total cost in dollars for buying x gallons of gas and a wash is: Total Cost = (# of gallons)* $1.59 + $6.75 I got this by taking the following two equations from the chart: 14.7 = (cost per gallon)* 5 + (cost of car wash) and 22.65 = (cost per gallon)* 10 + (cost of car wash) I then isolated (cost per gallon) in the first equation and used substitution to find the value of (cost of car wash). I then used the value of (cost of car wash) to solve for (cost per gallon). Let me know if you want further clarification on this procedure. b) The derivative model is going to be just y'=$1.59 since the derivative of 1.59x+6.75 is 1.59. c) Let us use the model to complete the table: For 12.5 gal: total cost = $1.59 * 12.5 gal + $6.75 total cost = $26.625 For 27.5 gal: total cost = $1.59 * 27.5 gal + $6.75 total cost = $50.475 d. The price per gallon of gas is the slope of the y=mx+b equation or $1.59. e. The price of the car wash is the y intercept of the y=mx+b equation or $6.75. One way to see this is that if you calculated how much the cost would be for getting zero gallons of gas using the model, the result would be the y intercept value or $6.75 Search Terms linear equations Please ask for clarification of any part before rating this answer. Best of luck! -blinkwilliams
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