The price of a cellular telephone plan is based on peak and nonpeak service. Kelsey used 45 peak minutes and 50 nonpeak minutes
and was charged $27.75. That same month, Mitch used 70 peak minutes and 30 nonpeak minutes and was charged $36. What are the rates per minute for peak and nonpeak time? Show your work.
We can build a system of two linear equations with two unknowns with the info provided in the problem, one with Kelsey info and one with Mitch info like so: Lets call p the amount on peak minutes and n the amount of non-peak minutes: 45p + 50n = 27.75 70p + 30n = 36 lets reduce the equations dividing the first by 5: 9p + 10n = 5.55 <span>70p + 30n = 36 </span>now, to eliminate n, lets multiply the first equation by -3 and add the two equations: -27p - 30n = -16.65 <span>70p + 30n = 36 </span>---------------------------- 43p + 0 = 19.35 p = 19.35<span>/43 p = 0.45 therefore the peak rate is $0.45 per minute lets substitute in one of the original equations this result: </span><span>45p + 50n = 27.75 </span>45(0.45) + 50n = 27.75 20.25 <span>+ 50n = 27.75 50n = 27.75 - 20.25 50n = 7.5 n = 7.5/50 n = 0.15 therefore the non-peak rate per minute is $0.15</span>
