Question

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.

Answer 1

B.The expression 75ℎ represents the total charge for Elegance Home Architects.

D.If the Johnson family hires the design firm for 15 hours, then Elegance Home Architects will be cheaper.

E.If the Johnson family hires the design firm for 40 hours, then Rock the House Digital Designs will be cheaper.

Explanation:

Which of the following statements are true? Select all that apply.

A.The expression 50ℎ represents the total charge for Rock the House Digital Designs.

B.The expression 75ℎ represents the total charge for Elegance Home Architects.

C.The cost for using Rock the House Digital Designs for an initial consultation only is $550.

D.If the Johnson family hires the design firm for 15 hours, then Elegance Home Architects will be cheaper.

E.If the Johnson family hires the design firm for 40 hours, then Rock the House Digital Designs will be cheaper.

Answer:

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. If they are hired for h hours, the total charge for Rock the House Digital Designs would be:

Total charge for Rock the House Digital Designs = 500 + 50h

Elegant Home Architects charge $75.00 per hour for the house plans, if they work for h hours, the total charge would be:

Total charge for Elegance Home Architects = 75h

A) Option A is not correct since the total charge for Rock the House Digital Designs is 500 + 50h

B) Option B is correct because the total charge for Elegance Home Architects = 75h

C) Option C is not correct, For an initial consultation, the cost for using Rock the House Digital Designs is $500

D) For a period of 15 hours:

Total charge for Rock the House Digital Designs = 500 + 50h = 500 + 50(15) = $1250

Total charge for Elegance Home Architects = 75h = 75(15) = $1125

Option D is correct because Elegance home architect would be cheaper

E) For a period of 40 hours:

Total charge for Rock the House Digital Designs = 500 + 50h = 500 + 50(40) = $2500

Total charge for Elegance Home Architects = 75h = 75(40) = $3000

Option D is correct because Rock the House Digital Designs would be cheaper