Question 1132796
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You have two pieces of information which you can use to write equations involving the numbers of adult (x) and child (y) tickets:<br>
(1) x+y = 50  the total number of tickets was 50
(2) 5x+2y = 190  the total cost of the tickets -- $5 per adult and $2 per child -- was 190<br>
You have two responses, in both of which the tutors solved the system of equations  by substitution -- solving one equation for one of the variables and substituting the expression for that variable in the other equation.<br>
That is one of the two most common methods for solving a system of two equations.  One of the tutors even says that substitution is the easiest method.<br>
For me, when both of the equations are in the form they are for this problem, the easiest method is elimination.<br>
With the method of elimination, you modify the given equations in such a way that either adding them or subtracting one from the other eliminates one of the variables.<br>
So my chosen path for solving the system of equations for this problem would be this:<br>
double equation (1):  x+y = 50  -->  2x+2y = 100
subtract this new equation from the second given equation:
(5x+2y)-(2x+2y) = 190-100
3x = 90
x = 30<br>
Then x=30 and x+y=50  -->  y = 20<br>
ANSWER: 20 adults and 30 children<br>
Note you should understand both methods for solving systems of equations.  Which one is easiest will depend on the individual student.<br>
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Again tutor @MathTherapy has proclaimed that he is better than anyone else, by saying that substitution is much easier than elimination for this problem, and that you should not let anyone tell you otherwise.<br>
Ignore his arrogant and absurd proclamations.  Learn both methods and use whichever one suits you for a particular problem.