The total cost of Anja's trip to the dentist was $628.35. She paid a flat fee of $89.95 which included the checkup and cleaning and then had 4 cavities filled, each of which cost the same amount. Which shows the correct equation and value of [tex]$x$[/tex], the cost of each cavity filling?
A. [tex]4 x+89.95=628.35 ; x=$134.60[/tex]
B. [tex]4(89.95)+x=628.35 ; x=$26855[/tex]
C. [tex]4 x+89.95=628.35 ; x=$179.58[/tex]
D. [tex]4(89.95)+x=628.35 ; x=$538.40[/tex]
Answer (2)
Set up the equation: 89.95 + 4 x = 628.35 , where x is the cost of each cavity filling.
Subtract the flat fee from the total cost: 4 x = 628.35 − 89.95 = 538.40 .
Divide by 4 to find the cost of each cavity filling: x = 4 538.40 = 134.60 .
The cost of each cavity filling is $134.60 .
Explanation
Problem Analysis Let's analyze the problem. Anja's total dentist bill was $628.35. This includes a flat fee of $89.95 for the checkup and cleaning, plus the cost of filling 4 cavities. We need to find the cost of each cavity filling, which we'll call x .
Setting up the Equation We can set up an equation to represent the total cost. The equation will be: Flat fee + 4 × Cost of each cavity filling = Total cost Substituting the given values, we get: 89.95 + 4 x = 628.35
Isolating the Variable Term Now, let's solve for x . First, subtract 89.95 from both sides of the equation: 4 x = 628.35 − 89.95 4 x = 538.40
Solving for x Next, divide both sides by 4 to find the value of x :
x = 4 538.40 x = 134.60
Finding the Solution So, the cost of each cavity filling is $134.60. The correct equation is 4 x + 89.95 = 628.35 , and the value of x is $134.60.
Examples
Imagine you're planning a group visit to an amusement park. There's a flat entrance fee, and then each ride costs an additional amount. Knowing the total cost and the flat fee, you can calculate the cost per ride. This is similar to Anja's dentist visit, where you have a flat fee for the checkup and then a cost per cavity filled. Understanding how to set up and solve these types of equations helps in budgeting and understanding costs in various real-life scenarios, from planning events to managing expenses.
The cost of each cavity filling is $134.60, calculated using the equation 89.95 + 4 x = 628.35 . By isolating x , we found that x = 134.60 . Thus, the correct choice is option A.
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