.
members of the Benton Youth club attended a major-league baseball game.
buying a total of 29 bleacher and lower reserved seats.
Ticket prices are shown in the table below the total cost of the tickets was $ 913.
how many of each kind of ticket was bought?
lower reserved $32
Bleacher $31
~~~~~~~~~~~~~~~~~~
Let x be the number of the lower reserved tickets.
Then the number of bleacher seats tickets is (29-x).
Total money for the seats is 32x + 31*(29-x).
The total money equation is
32x + 31*(29-x) = 913.
Simplify and find x
32x + 31*29 - 31x = 913
32x - 31x = 913 - 31*29
x = 14.
ANSWER. 14 lower reserved tickets and the rest 29-14 = 15 are bleacher seats tickets.
CHECK. 14*32 + 15*31 = 913 dollars, total. ! Correct !
Solved.
--------------
In this post, I showed you the solution procedure, starting from one-equation setup.
There is another way to setup the problem using two equations
x + y = 29 (1) (counting number of tickets)
32x + 31y = 913 (2) (counting total money)
If you start with two equation, then next step is to express
y = 29 - x
and substitute it into equation (2)
32x + 31*(29-x) = 913.
Doing this way, you get the same equation as the starting equation in one-equation setup.
So, you just know how to proceed further from this point . . .
Thus you may use / (you may start from) any of these two setup versions - it is on your choice,
and you should follow to the method accepted in your class.
In such problems, one-equation setup usually provides a shorter way to the answer.
But a good student should know both one-equation and two-equations setup and solution procedures.
In any case, you just have everything that you need to know when you start learning this subject.
///////////////
It is a standard and typical tickets problem.
There are different methods of solving such problems.
In this site, there is a lesson
- Using systems of equations to solve problems on tickets
explaining and showing different methods of solving such problems.
From this lesson, 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.