SOLUTION: Miscellaneous Problem: A museum charges $5 for admission ticket, but members receive a $1 discount and students are admitted for half price. One Saturday, 1,050 tickets were sol

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Question 875436: Miscellaneous Problem:
A museum charges $5 for admission ticket, but members receive a $1 discount and students are admitted for half price. One Saturday, 1,050 tickets were sold for a total of $4,035. If 35 more students' tickets than full price tickets were sold, find number of each type of tickets sold.
Answer by josgarithmetic(39628) About Me  (Show Source):
You can put this solution on YOUR website!
Normal charge, $5
Members, $4
Students, $2.5

x, y, z, for count of tickets sold as Normal, Members, Students.

5x%2B4y%2B2.5z=4035 and x%2By%2Bz=1050.
The additional ticket relationship description means z-x=35, which is equivalent to -x%2B0%2Ay%2Bz=35.

You can use a matrix,


I used an online matrix calculator, http://www.math.purdue.edu/~dvb/gaussian.php ,
and found these results:
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x=225
y=565
z=260
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