QQuestionMathematics
QuestionMathematics
The total cost of renting a cotton candy machine for 4 hours is $72. What equation can be used to model the total cost y for renting the cotton candy machine x hours?
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Answer
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Step 1:: Identify the given information and the unknown.
The total cost of renting a cotton candy machine for 4 hours is $72. We want to find an equation that models the total cost y for renting the cotton candy machine x hours.
Step 2:: Understand the problem context.
The relationship between the cost of renting the cotton candy machine and the number of hours is directly proportional, meaning that as the number of hours increases, the total cost also increases.
Step 3:: Set up the equation.
y = kx
Since the relationship is directly proportional, we can use the formula: where: - y is the total cost - x is the number of hours rented - k is the constant of proportionality
Step 4:: Determine the constant of proportionality.
k = \frac{72}{4} = 18
We are given that the total cost for renting the cotton candy machine for 4 hours is $72. We can use this information to find the constant of proportionality: Now, divide both sides by 4 to solve for k:
Step 5:: Plug the constant of proportionality back into the equation.
y = 18x
Now that we have determined the constant of proportionality, we can plug it back into our original equation:
Final Answer
The equation that models the total cost y for renting the cotton candy machine x hours is y = 18x.
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