To determine the correct equation and the value of [tex]\( x \)[/tex], the cost of each cavity filling, let's break down the problem logically and solve it step by step.
### Given Information:
- Total cost of the trip: \[tex]$628.35
- Flat fee for checkup and cleaning: \$[/tex]89.95
- Number of cavities filled: 4
### Step 1: Set up the Equation
Let's denote the cost of filling one cavity as [tex]\( x \)[/tex].
The total cost is the sum of the flat fee and the cost of filling the cavities. Since there are 4 cavities, the cost of filling them would be [tex]\( 4x \)[/tex].
Thus, the equation can be set up as:
[tex]\[ \text{Total cost} = \text{Flat fee} + \text{Cost per cavity} \times \text{Number of cavities} \][/tex]
[tex]\[ 628.35 = 89.95 + 4x \][/tex]
This matches the equation:
[tex]\[ 4x + 89.95 = 628.35 \][/tex]
### Step 2: Solve for [tex]\( x \)[/tex]
To find [tex]\( x \)[/tex], we need to isolate [tex]\( x \)[/tex] in the equation:
[tex]\[ 4x + 89.95 = 628.35 \][/tex]
Subtract the flat fee from the total cost:
[tex]\[ 4x = 628.35 - 89.95 \][/tex]
[tex]\[ 4x = 538.40 \][/tex]
Divide both sides by 4 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{538.40}{4} \][/tex]
[tex]\[ x = 134.60 \][/tex]
### Step 3: Verify the Choices
Let's compare our equation and the calculated value of [tex]\( x \)[/tex] with the given choices:
1. [tex]\( 4x + 89.95 = 82835 ; x = 13480 \)[/tex]
2. [tex]\( 4(8995) + x = 628.35 \)[/tex]
3. [tex]\( 4x + 89.95 = 628.35 ; x = 179.58 \)[/tex]
4. [tex]\( 4(89.95) + x = 628.35 ; x = 538.40 \)[/tex]
The correct equation from our setup is:
[tex]\[ 4x + 89.95 = 628.35 \][/tex]
The correct value of [tex]\( x \)[/tex] we calculated is:
[tex]\[ x = 134.60 \][/tex]
None of the given choices present the correct combination of the equation and the value, but our calculations confirm:
[tex]\[ 4x + 89.95 = 628.35 ; x = 134.60 \][/tex]
Given the curriculum and typical response format, always double-check your input data and parameters if you encounter discrepancies.
