Question 1151868: Mario's Marionettes donated free tickets for their show to the local day care centre. They claimed that value of these tickets was $176.75. A child's ticket cost $5.50 and an adult ticket cost $8.75. If there were three times as many children's ticket as adult tickets, how many adults and children got to attend the show for free?
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
Let A be the number of adult tickets.
Then the number of children tickets is (3A), according to the condition.
And the revenue equation is then
5.50*(3A) + 8.75*A = 176.75 dollars.
Simplify ans solve for A
A =  = 7.
ANSWER. 7 adult tickets and 3*7 = 21 children tickets.
CHECK. 7*8.75 + 21*5.50 = 176.75 dollars. ! Precisely correct !
Solved.
You (and me) may retell the same solution in other words.
According to the condition, you can group all visitors in sets in a way that ech set contains 1 adult and 3 children.
The cost of rickets for each such group will be 8.75 + 3*5.50 dollars = 25.25 dollars.
The number of such groups will be  .
When you divide using your computer, you will get the number of 7.
So, there are 7 such groups.
It means that there are 7 adults and 7*3 = 21 children, in all.
So, you solved the problem by different way.
Solved ? --- No, simply re-told the same Algebra solution in other words.
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Every day we solve 3 - 5 - 7 such problems at the forum.
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.
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