Question

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. Thank you!

   

Answer 1

As you have read in book.. you have to solve these 2 equations.

A: $19 + $0.45D + $0.28E

B: $19 + $0.59D + $0.12E

These are total cost of plan A and B respectively.

the agent would be indifferent between the two plans when cost of both the plans are same i.e

$19 + $0.45D + $0.28E = $19 + $0.59D + $0.12E

0.14D = 0.16E

D = 8/7E

D = 1.143E

now as we need to find percentage of minutes so we assume Evening houre (E) = 100

which gives D = 114.3 hours

percent of D = 114.3/(114.3+100) = 53.33%

this can also be found out without multiplying by 100

then D = 1.143/(1.143+1) = 53.33