SOLUTION: There were 345 tickets purchased for a major league baseball game. The lower reserved  tickets cost ​$9.50 and the upper reserved tickets cost ​$8.00. The total amount of m

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Question 1137198: There were 345 tickets purchased for a major league baseball game. The lower reserved  tickets cost ​$9.50 and the upper reserved tickets cost ​$8.00. The total amount of money spent was ​$2809.50. How many of each kind of ticket were​ purchased?
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
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Let x = # of lower reserved tickets, y = # of upper reserved tickets.


From the condition, you have these 2 equations


         x +      y = 345        (1)    (counting tickets)

    9.50*x + 8.00*y = 2809.50    (2)   (counting money)


From equation (1), express  y = 345 - x  and substitute it into equation (2), You will get


    9.50x + 8*(345-x) = 2809.50.


Express x and calculate answer


    x =  = 33.


Then from equation (1),  y = 345 - 33 = 312.


ANSWER.  33 lower reserved tickets and 312 upper reserved tickets.


CHECK.   33*9.50 + 312*8 = 2809.50 dollars.   ! Correct !

The problem solved using 2-equation setup and the Substitution method.

--------------

It is a standard and typical ticket problem.

For ticket problems,  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 and 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".


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