We can set up an equation to represent the total cost Lauren paid.

The total cost is made up of:

• The cost for labor (charged per hour),
• The cost for parts.

The technician worked for 3.75 hours and charged a certain amount $x$ per hour for labor. Additionally, Lauren was charged $119 for the parts.

The total cost was $400.25, so we can set up the equation:

$3.75x + 119 = 400.25$

Solving for $x$ (the cost of labor per hour):

1. Subtract $119 from both sides: $3.75x = 400.25 - 119$ $3.75x = 281.25$

2. Divide both sides by 3.75: $x = \frac{281.25}{3.75}$ $x = 75$

So, the cost of labor per hour is $75.

Would you like more details on this solution or have any questions?

Here are 5 related questions to explore:

1. What would the total cost be if the labor rate was $80 per hour instead?
2. How would the equation change if the technician worked 4 hours instead of 3.75?
3. If Lauren's budget was $350, what should the maximum labor cost per hour be?
4. What would happen to the total cost if the cost of parts increased by 20%?
5. How long would the technician need to work to make the total $500?

Tip: Always double-check your work by substituting the value of $x$ back into the original equation!