Question

5a. attorney a charges a fixed fee on $250 for an initial meeting and $150 per hour for all hours worked after that. attorney b charges $150 for the initial meeting and $175 per hour. in how many hours will they cost the same? whats the total cost? 5b. you have $200 in the savings account and save $10 per week and your friend has $55 in his account and saves $15 per week. how many weeks will it take for you and your friend to have the same balance? what is the total savings?

Explanation:

Step1: Set up equations for Attorney A and B

Let $x$ be the number of hours worked after the initial meeting.
For Attorney A, the cost $C_A=250 + 150x$.
For Attorney B, the cost $C_B = 175x$.

Step2: Set $C_A = C_B$ and solve for $x$

$250+150x=175x$.
Subtract $150x$ from both sides: $250 = 175x-150x$.
$250 = 25x$.
Divide both sides by 25: $x=\frac{250}{25}=10$ hours.

Step3: Calculate the total cost

Substitute $x = 10$ into either $C_A$ or $C_B$. Using $C_A$: $C_A=250+150\times10=250 + 1500=1750$.

Step4: Set up equations for savings

Let $y$ be the number of weeks.
Your savings $S_1=200 + 10y$.
Your friend's savings $S_2=55+15y$.

Step5: Set $S_1 = S_2$ and solve for $y$

$200 + 10y=55+15y$.
Subtract $10y$ from both sides: $200=55 + 15y-10y$.
$200=55 + 5y$.
Subtract 55 from both sides: $200 - 55=5y$.
$145 = 5y$.
Divide both sides by 5: $y=\frac{145}{5}=29$ weeks.

Step6: Calculate the total savings

Substitute $y = 29$ into either $S_1$ or $S_2$. Using $S_1$: $S_1=200+10\times29=200 + 290=490$.

Answer:

5a. 10 hours, total cost is $1750.
5b. 29 weeks, total savings is $490.