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 with setting up equation for attorney b

For 5 hours they both will cost the same amount.

Step-by-step 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.

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6     6   6

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