.
Write equations as you read the problem
x - y = 50 (1)
5x + 2y = 950 (2)
First equation comes from counting persons.
Second equation comes from counting money.
There are several different methods to solve.
For example, using the Elimination method, multiply first equation by 2 (all the terms in both sides);
keep equation (1) as is.
2x - 2y = 100 (3)
5x + 2y = 950 (4)
Now add the equations. The terms "-2y" and "2y" will cancel each other, and you will get
a single equation in only one unknown x
2x + 5x = 100 + 950,
or
7x = 1050,
x = 1050/7 = 150.
Then from equation (1), y = x - 50 = 150 - 50 = 100.
ANSWER. 150 adults and 100 students.
CHECK. 5*150 + 2*100 = 750 + 200 = 950 dollars (t0tal money). ! Correct !
Solved.
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It is a standard and typical tickets problem.
There are different methods of solving such problems. See the lessons in this site
- 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.