The Johnson family is going to build a new home. They need to have working drawings of their house plans created by a design firm. They will choose between Rock the House Digital Designs and Elegant Home Architects. Rock the House Digital Designs charges $500.00 for the initial consultation with the Johnson family, plus $50.00 for every additional hour of work for the house plans. Elegant Home Architects charge $75.00 per hour for the house plans. Let ℎ represent the number of hours for which the Johnson family hires the design firm. Which of the following statements are true? Select all that apply.

The Elegant Home Architects charges are less than Rock the House Digital Designs charges for hours worked more than 2.

If the number of hours worked is equal to 2 than both would charge the same and if the hours are less than 2 then  Rock the House Digital Designs  will be a better option .

Step-by-step explanation:

Let ℎ represent the number of hours for which the Johnson family hires the design firm.

Suppose the  Johnson family hires the design firm for ten hours so h= 10

Then the charges by the Rock the House Digital Designs will be

$ 500 + 50(10)= $ 500+ $500= $1000

And the charges for the services by Elegant Home Architects will be

$75.00(10) = $ 750

Therefore the Elegant Home Architects charges are less than Rock the House Digital Designs charges.

But if the number of hours worked is equal to 2 than both would charge the same and if the hours are less than 2 then  Rock the House Digital Designs  will be a better option .

Rock the House Digital Designs

For 2 hours

$ 500 + 50(2)= $300

For 1 Hour

$500 + 50 (1)= $ 550

Elegant Home Architects

For 2 hours

$75.00(2) = $ 300

For 1 Hour

$75.00(1) = $ 75