The total cost of gasoline varies directly with the number of gallons purchased. Edie pays $22.68 for 12 gallons of gasoline. Which equation shows the relationship between the total cost of gasoline, $c$, and the number of gallons purchased, $n$?
A. $c=22.68 n$
B. $c=1.89 n$
C. $n =1.89 c$
D. $n=22.68 c$
Answer (2)
Recognize that the relationship between cost c and number of gallons n is a direct variation, so c = kn .
Substitute the given values c = 22.68 and n = 12 into the equation to find the constant of proportionality k .
Calculate k == 1.89 .
Write the equation as c = 1.89 n , so the answer is c = 1.89 n .
Explanation
Understanding the Problem The problem states that the total cost of gasoline, c , varies directly with the number of gallons purchased, n . This means that there is a constant of proportionality, k , such that c = k . We are given that Edie pays 22.68 f or 12 g a ll o n so f g a so l in e . W ec an u se t hi s in f or ma t i o n t o f in d t h e v a l u eo f k$.
Setting up the Equation We are given that when n = 12 , c = 22.68 . Substituting these values into the equation c = kn , we get: 22.68 = k .
Solving for k To find the value of k , we divide both sides of the equation by 12: k = .
Finding the Equation Performing the division, we find that k = 1.89 . Therefore, the equation that relates the total cost c and the number of gallons n is c = 1.89 n .
Final Answer The equation that shows the relationship between the total cost of gasoline, c , and the number of gallons purchased, n , is c = 1.89 n . This corresponds to option B.
Examples
Understanding direct variation is useful in many real-life scenarios. For example, if you are paid an hourly wage, your total earnings vary directly with the number of hours you work. If you earn $15 per hour, your total earnings, E , can be represented as E = 15 h , where h is the number of hours you work. Similarly, in cooking, if a recipe calls for a certain amount of ingredients for a certain number of servings, you can use direct variation to adjust the recipe for a different number of servings.
The relationship between the total cost of gasoline and the number of gallons purchased is expressed by the equation c = 1.89 n . This indicates that for every gallon of gasoline, the cost is $1.89. Therefore, the correct answer is Option B: c = 1.89 n .
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