A real estate agent is considering changing her cell phone plan. There are three plans to choose from, all of which involve a monthly service charge of $19. Plan A has a cost of $0.45 a minute for daytime calls and $0.28 a minute for evening calls. Plan B has a charge of $0.59 a minute for daytime calls and $0.12 a minute for evening calls.
Q: Suppose that the agent expects both daytime and evening calls. At what point (i.e., percentage of call minutes for daytime calls) would she be indifferent between plans A and B?
According to answers in the book I need to solve the following formula.
A: $19 + $0.45D + $0.28E
B: $19 + $0.59D + $0.12E
"Setting these equal and solving, D = 1.143 E. Thus, if E = 100 minutes, then D = 114 minutes. Hence, for 53.33 percent daytime minutes, the agent would be indifferent between the two plans."
How exactly do I solve the above ot get the 1.143, 100 and 53.33? Please include step-by-step solution if you would like to be rated.