A software consultant charges an enterprise client a fixed setup fee of 200 dollars plus a… — GMAT

A software consultant charges an enterprise client a fixed setup fee of $200$ dollars plus an hourly rate of $r$ dollars for 1-on-1 technical training. For team training workshops, the consultant charges a fixed setup fee of $400$ dollars plus an hourly rate that is $50\%$ higher than the 1-on-1 rate. If the client was billed a total of $2,400$ dollars for $12$ hours of 1-on-1 training and $8$ hours of team training workshops, what is the value of $r$ ?

Answer: 75 dollars per hour

Answer

The individual hourly rate

r

75

dollars per hour.

The total cost consists of fixed setup fees (

200 + 400 = 600

) and variable hourly charges (

12r + 8 \times 1.5r = 24r

). Setting the total cost

600 + 24r

equal to

2,400

and solving for

r

yields

r = 75

Step-by-Step Solution

Formulate the total cost equation for the 1-on-1 technical training.

\text{Cost}_{\text{1-on-1}} = 200 + 12r

The client pays a

200

dollar setup fee plus

r

dollars for each of the

12

hours.

Determine the hourly rate and total cost equation for the team training workshops.

\text{Hourly Rate}_{\text{team}} = 1.5r

, so

\text{Cost}_{\text{team}} = 400 + 8(1.5r) = 400 + 12r

The team hourly rate is

50\%

greater than

r

, which equals

r + 0.5r = 1.5r

. Multiplying by

8

hours yields

12r

in hourly fees, plus the

400

dollar setup fee.

Combine the total costs to create a single linear equation in terms of

r

(200 + 12r) + (400 + 12r) = 2400 \implies 600 + 24r = 2400

The total amount billed across both services is given as

2,400

dollars.

Isolate the variable

r

and calculate its numerical value.

24r = 1800 \implies r = 75

Subtracting

600

from both sides gives

24r = 1800

, and dividing by

24

yields

r = 75

Key Concept

Linear Equations in One and Two Variables

Estimated Time:1m 30s

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