Question

The attorney A, charges a fixed fee on $250 for an initial meeting and $150 per hour for all hours worked after that. The attorney B, charges $200 for one hour and $800 for five hours. For how many hours will they both cost the same amount? This is a systems of equations problem.

So far I have y = cost and x = hours

For attorney A, the equation would be y = 250 + 150x

Need help with setting up equation for attorney B

Answer 1

For 5 hours they both will cost the same amount.

Explanation:

Here, let us assume for m hours, both attorneys cost the same amount y.

For Attorney A:

The fixed fee = $250

The per hour rate = $ 150

So, the cost for m hours = m ( Cost of 1 hour ) = m ( $150) = 150 m

Now, the total fees of Attorney A for m hours = Fixed fee + m hour charges

y = $250 + 150 m ............... (1)

For Attorney B:

The fixed fee = $200

The 5 hour rate = $ 800

⇒ Per hour rate = $800/ 5 = $160

So, the cost for m hours = m ( Cost of 1 hour ) = m ( $160) = 160 m

Total fees of Attorney B for m hours = Fixed fee + m hour charges

y = $200 + 160 m .......... (2)

Now comparing (1) and (2) , we get :

$250 + 150 m = $200 + 160 m

or, 250 - 200 = 160 m - 150 m

or, 10 m = 50

or, m = 50 / 10 = 5, ⇒ m = 5

Hence, for 5 hours they both will cost the same amount.