SOLUTION: at a travel agency the cost of a trip to Mexico is $350 for an adult and 200 for child one month the travel agency sold 50 trips of these trips, y trips were for children the trave

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: at a travel agency the cost of a trip to Mexico is $350 for an adult and 200 for child one month the travel agency sold 50 trips of these trips, y trips were for children the trave      Log On


   

Question 1108699: at a travel agency the cost of a trip to Mexico is $350 for an adult and 200 for child one month the travel agency sold 50 trips of these trips, y trips were for children the travel agency collected c dollars for selling 50 trips. Write a linear equation for c in terms of y. Express y in terms of c and if $15,250 was collected, find the number of children going on the trip
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39631) About Me  (Show Source):
You can put this solution on YOUR website!
y children
50-y adults, 50 combined adults and children
c=15250

350%2850-y%29%2B200y=c

Do the algebra steps,...

cross%28y=-c%2F150%2B116%262%2F3%29
-
recheck:350%2A50-350y%2B200y=c
350%2A50-150y=c
-150y=c-350%2A50
y=%28-c%2B350%2A50%29%2F150
-
y=%28-15250%2B350%2A50%29%2F150=15, fifteenchildren


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Substituting for c, and evaluating y,
highlight%28cross%28y=5%29%29----------five children

Answer by ikleyn(52925) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let c = # of children.


The "money" equation is

c*200 + (50-c)*350 = 15250.

200c + 50*350 - 350c = 15250,

-150c = 15350 - 30*350 = 4850  ====>  c = %28-4850%29%2F%28-150%29 = 15.


Answer.  15 children and 50-15 = 35 adults.


Check.   15*200 + 35*350 = 15250 dollars.   ! Correct !

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To see other similar solved problems on tickets,  look into the lessons
    - Using systems of equations to solve problems on tickets
    - Three methods for solving standard (typical) problems on tickets
in this site.

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".


Save the link to this online textbook together with its description

Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson

to your archive and use it when it is needed.

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Be aware !   The solution and the answer  ("5 children")  by  @josgarithmetic  both are   W R O N G.