Question

Attorney A charges a fixed fee on $250 for an initial meeting and $150 per hour for all hours worked after that. Write an equation in slope-intercept form. Attorney B charges $150 for the initial meeting and $175 per hour. Find the charge for 26 hours of work for each attorney. Which is the better deal? At how many hours does this attorney become a better deal?

Answer 1

let h be the number of hours then

A → C = 150h + 250 ( where C is charge )

B → C = 175h + 150

for 26 hours

A → C = (150 × 26 ) + 250 = 3900 + 250 = $4150

B → C = (175 × 26 ) + 150 = 4550 + 150 = $4700

Attorney A is cheaper for 26 hours, thus better deal

Equate the 2 equations to find hours they charge the same

175h + 150 = 150h + 250 ( subtract 150h from both sides )

25h + 150 = 250 ( subtract 150 from both sides )

25h = 100 ( divide both sides by 25 )

h = 4 ← number of hours when charges for both are equal

Thus Attorney A becomes a better deal at 5 hours

Answer 2

Using the slope - intercept relationship, the charges for each attorney is :

• y = 150h + 250 - - - Attorney A
• y = 175h + 150 - - - - Attorney B
• Attorney A is better at 5 hours.

General form of a slope - intercept equation :

• y = bx + c

• Rate per hour = b
• Fixed fee = c

Attorney A :

• y = 150h + 250

Attorney B:

• y = 175h + 150

Cost of each attorney for a 26 hour work :

Attorney A :

y = 150(26) + 250 = $4150

Attorney B :

y = 175(26) + 150 = $4700

Hence, the better deal is Attorney A

Hours when Attorney A becomes the better deal :

150h + 250 < 175h + 150

250 - 150 < 175h - 150h

100 < 25h

4 < h or h > 4

After 4 hours,

Therefore, Attorney A becomes the better deal at five hours.

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