Question

Landscaping company A charges a $50 fee plus $18 an hour and landscaping company B charges $20 per hour and a fee of $30. At how many hours will the cost be the same for both companies

Answer 1

$\text{Hello there!}\\\\\text{In this question, we're trying to find when both companies cost the same}\\\\\text{We know that landscaping company A charges \ 50 fee plus \ 18 an hour}\\\\\text{That would be represented as:}\,\,y=18x+50\\\\\text{We know that landscaping company B charges \ 20 per hour and a \ 30 fee}\\\\\text{That would be represented as:}\,\,y=20x+30\\\\\text{We would get both equations, put them together, and solve}\\\\18x+50=20x+30\\\\\text{Solve:}\\\\18x+50=20x+30$

$\text{Subtract both sides by -20x}\\\\-2x+50=+30\\\\\text{Subtract both sides by 50}\\\\-2x=-20\\\\\text{Divide by -2}\\\\\large\boxed{x=10}\\\\\text{They're the same price at 10 hours}\\\\\text{I hope this helps!}\\\text{Best regards,}\\\text{MasterInvestor}$