SOLUTION: The total number of passengers riding a certain city bus during the morning shift is 1300. If the child's fare is $0.50, the adult fare is $1.50, and the total revenue from the far

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The total number of passengers riding a certain city bus during the morning shift is 1300. If the child's fare is $0.50, the adult fare is $1.50, and the total revenue from the far      Log On


   

Question 1127503: The total number of passengers riding a certain city bus during the morning shift is 1300. If the child's fare is $0.50, the adult fare is $1.50, and the total revenue from the fares in the morning shift is $1450, how many children and how many adults rode the bus during the morning shift?
children
adult
Found 3 solutions by josgarithmetic, ikleyn, addingup:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
c children
a adults

system%28c%2Ba=1300%2C0.5c%2B1.5a=1450%29

Money equation,
c%2B3a=2900

system%28c%2Ba=1300%2Cc%2B3a=2900%29

Subtract E1 from E2.
2a=1600
highlight%28a=800%29-------adult tickets

highlight%28500%29--------children

Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the number of adults under the question.

Then the number of children is (1300-x).


The money equation is


    0.5*(1300-x) + 1.50*x = 1450    dollars.


Simplify and solve for x step by step :


    650 - 0.5x + 1.5x = 1450

    1.5x - 0.5x = 1450 - 650

    x = 800.


Answer.  800 adults and 1300 - 800 = 500 children.


Check.   0.5*500 + 1.5*800 = 1450  dollars.    ! Correct !

Solved.

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It is a standard ticket problem.

Read the lessons
    - Using systems of equations to solve problems on tickets
    - Three methods for solving standard (typical) problems on tickets
in this site.

From these lessons,  learn on how to solve such problems once for all.

Also,  you have this free of charge online textbook in ALGEBRA-I in this site
    - ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lessons are the part of this online textbook under the topic "Systems of two linear equations in two unknowns".


Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
a + c = 1300
so if we substract the adults what's left is children:
c = 1300 - a
~~~~~~~~~~~~~~~~~~~~~~~~~~
1.50a + 0.50c = 1450
substitute for c:
1.5a + 0.50(1300 - a) = 1450
1.5a + 650 - 0.50a = 1450
1a = 1800
a = 800 this is the number of adults
The children:
1300 - 800 = 500 children
:
Happy learning!