Question

A company is looking to hire a lawyer. One law firm states that their legal fees can be determined using the expression 370x + 25000, where x is the number of hours of legal assistance. A second law firm states that their legal fees can be determined using the expression 480x + 21000. The company president wants to know when the legal fees would cost the same for each law firm. What number of hours of legal assistance makes the equation 370x + 25000 = 480x + 21000 true? Round your answer to the nearest whole number.

Answer 1

The number of hours of legal assistance that makes the equation 370x + 25000 = 480x + 21000 true is 36.

Step-by-step explanation:

To find the number of hours of legal assistance that makes the equation 370x + 25000 = 480x + 21000 true, we need to solve for x. Here are the steps:

1. Subtract 480x from both sides of the equation: 370x + 25000 - 480x = 21000
2. Combine like terms: -110x + 25000 = 21000
3. Subtract 25000 from both sides of the equation: -110x = -4000
4. Divide both sides of the equation by -110 to isolate x: x = 36.3636

Since the number of hours cannot be a decimal, we round 36.3636 to the nearest whole number, which is 36. Therefore, when the number of hours of legal assistance is 36, the legal fees would cost the same for both law firms.