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 a 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

Statement 2, Statement 4, and Statement 5 all applies

Explanation:

Statement 1:

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

Rock the House Digital Designs:

Initial consultation charge of $500 + $50 for every additional hour of work for the house plans

500 + 50h

NOT TRUE

Statement 2:

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

Elegance Home Architects:

$75 per hour for the house plans

75h

TRUE

Statement 3:

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

The cost for using Rock the House Digital Designs for an initial consultation only is $500

NOT TRUE

Statement 4:

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

Rock the House Digital Designs = 500 + 50h

500 + 50(15)

= 500 + 750

= $1,250

Elegance Home Architects = 75h

= 75(15)

= $1,125

TRUE

Statement 5:

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

Rock the House Digital Designs = 500 + 50h

= 500 + 50(40)

= 500 + 2,000

= $2,500

Elegance Home Architects = 75h

= 75(40)

= $3,000

TRUE