Let's work through the problem step-by-step to determine the correct solution.
### Step 1: Understand the charges
- The plumber charges a fixed fee of \[tex]$45 just to come to the house.
- Additionally, the plumber charges per hour for the work done.
- The total charge for the visit is \$[/tex]250.
### Step 2: Set up the equation
Let [tex]\( x \)[/tex] represent the number of hours the plumber worked. The total cost can be expressed as the sum of the fixed fee and the cost for the hours worked:
[tex]\[ 45 + 50x = 250 \][/tex]
Here,
- \[tex]$45 is the fixed fee.
- \$[/tex]50 per hour is the hourly rate.
- \$250 is the total charge.
### Step 3: Solve the equation
To find [tex]\( x \)[/tex], we need to isolate it on one side of the equation. Let's solve for [tex]\( x \)[/tex] step-by-step:
1. Subtract 45 from both sides of the equation:
[tex]\[ 45 + 50x - 45 = 250 - 45 \][/tex]
[tex]\[ 50x = 205 \][/tex]
2. Divide both sides by 50:
[tex]\[ x = \frac{205}{50} \][/tex]
[tex]\[ x = \frac{41}{10} \][/tex]
[tex]\[ x = 4.1 \][/tex]
So, the plumber worked 4.1 hours.
### Step 4: Verify which option matches
From the options given:
- [tex]\[ 45x + 50 = 250 ; x = 4.4 \][/tex] hours (incorrect equation and answer)
- [tex]\[ 45x - 5 = 250 ; x = 6.7 \][/tex] hours (incorrect equation and answer)
- [tex]\[ 50x + 45 = 250 ; x = 4.1 \][/tex] hours (correct equation and answer)
- [tex]\[ 50x - 45 = 250 ; x = 5.9 \][/tex] hours (incorrect equation and answer)
The correct equation is [tex]\( 50x + 45 = 250 \)[/tex], and the correct solution is [tex]\( x = 4.1 \)[/tex] hours.
Therefore, the correct answer is:
[tex]\[ 50x + 45 = 250 ; x = 4.1 \text{ hours} \][/tex]
