Problema Solution
a total of 14,000 people ride a certain subway line during the morning rush hour. the ticket price for the a ride are 0.85 for students, 1.70 for adults, and 0.65 for senior citizens. and the revenue from these rides is 21.900. if the ticket price were raised to 0.95 for students and 2$ for adults, and the senior citizen price were unchanged, the expected revenue from these would be $25,600. how many riders in each category normally ride the subway during the morning rush hour
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let
s = the number of students
a = the number of adults
c = the number of senior citizens
a total of 14,000 people ride a certain subway line during the morning rush hour:
s + a + c = 14,000
the ticket price for the a ride are 0.85 for students, 1.70 for adults, and 0.65 for senior citizens. and the revenue from these rides is 21.900:
0.85s + 1.70a + 0.65c = 21,900
the ticket price were raised to 0.95 for students and 2$ for adults, and the senior citizen price were unchanged, the expected revenue from these would be $25,600:
0.95s + 2a + 0.65c = 25,600
by solving the system of equations:
s + a + c = 14000
0.85s + 1.70a + 0.65c = 21900
0.95s + 2a + 0.65c = 25600
by solving we find:
s = 1,000 students
a = 12,000 adults
c = 1,000 senior citizens
click here to see the step by step solution of the system of equations:
during the morning rush hour normally there are 1,000 students, 12,000 adults and 1,000 senior citizens.