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
70p + 30n = 36
now, to eliminate n, lets multiply the first equation by -3 and add the two equations:
-27p - 30n = -16.65
70p + 30n = 36

43p + 0 = 19.35
p = 19.35/43
p = 0.45
therefore the peak rate is $0.45 per minute
lets substitute in one of the original equations this result:
45p + 50n = 27.75
45(0.45) + 50n = 27.75
20.25 + 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