SOLUTION: If 116 people attend a concert and tickets for adults cost $3 while tickets for children cost $2.75 and total receipts for the concert was $335.25, how many of each went to the con

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Question 1161437: If 116 people attend a concert and tickets for adults cost $3 while tickets for children cost $2.75 and total receipts for the concert was $335.25, how many of each went to the concert?

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52770) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let's find the number of adults, x, first.


If the number of adults is x, then the number of children is (116-x).


Then your equation is for the total money

    3x + 2.75*(116-x) = 335.25.


From this equation

    x = %28335.25-2.75%2A116%29%2F%283-2.75%29 = 65 adults.


Then the number of children is 112-65 = 47.

Solved.

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It is a standard tickets problem.

There are different methods of solving such 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".

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!


A quick mental solution method; if formal algebra is not required....

(1) all 116 tickets at $3 each would bring in $348
(2) That $348 is $12.75 more than the actual total of $335.25
(3) The difference between the two ticket prices is $0.25
(4) The number of children's tickets sold, to bring the total down to the correct $335.25, is $12.75/$0.25 = 51

ANSWER: 51 children's tickets; 116-51 = 65 adult tickets

CHECK:
51(2.75)+65(3) = 140.25+195 = 335.25