SOLUTION: There were 164 tickets purchased for a major league baseball game. The lower box  tickets cost ​$12.50 and the upper box tickets cost ​$10.00. The total amount of money spe

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Question 1152852: There were 164 tickets purchased for a major league baseball game. The lower box  tickets cost ​$12.50 and the upper box tickets cost ​$10.00. The total amount of money spent was ​$1945.00. How many of each kind of ticket were​ purchased?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52778) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the number of the Lower box tickets.

Then the number of the Upper box tickets is (164-x).


The equation for the total is


    12.50x + 10*(164-x) = 1945.00.


It is your basic equation to find the value of x.


From the equation


    x = %281945-10%2A164%29%2F%2812.50-10%29 = 122.


ANSWER.  122 Lower box tickets and the rest, 164-122 = 42 Upper box tickets.


CHECK.  122*12.50 + 42*10.00 = 1945 dollars.    ! Precisely correct !

Solved.

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It is a standard tickets problem.

There are different methods of solving such problems.
In this site, there are lessons
    - Using systems of equations to solve problems on tickets
    - Three methods for solving standard (typical) problems on tickets
explaining and showing all basic methods of solving such problems.

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 lesson is 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.


Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


Here is a fast way to solve this and a large number of similar problems if a formal algebraic solution is not required:

(1) 164 tickets all at $10 would cost $1640.
(2) The actual total cost of the tickets was $1945; that is $305 more than the figure from (1).
(3) The difference between the costs of the two kinds of tickets is $2.50.
(4) The number of more expensive tickets is the $305 total from (2), divided by the $2.50 difference from (3): 305/2.5 = 610/5 = 1220/10 = 122.