A cell phone company charges $120 for the phone, and then $35 a month for phone service. Another cell phone company charges $55 a month for phone service with a free phone. After how many months will the phone services cost the same?
[tex]\text{Hello there!}\\\\\text{Turn the question into equations:}\\\\y=35x+120\\\\y=55x\\\\\text{Combine the equations and solve:}\\\\35x+120=55x\\\\\text{Subtract 55 from both sides}\\\\-20x+120=0\\\\\text{Subtract 120 from both sides}\\\\-20x=-120\\\\\text{Divide both sides by -20}\\\\x=6\\\\\boxed{\text{They will cost the same after 6 months}}}[/tex]
