SOLUTION: For a school play, students tickets cost 40 cents and adults tickets were 75 cents .the total receipts for 90 tickets were $46.50 .how many of each kind were sold ?

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Question 1043247: For a school play, students tickets cost 40 cents and adults tickets were 75 cents .the total receipts for 90 tickets were $46.50 .how many of each kind were sold ?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52775) About Me  (Show Source):
You can put this solution on YOUR website!
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For a school play, students tickets cost 40 cents and adults tickets were 75 cents .the total receipts for 90 tickets were $46.50 .how many of each kind were sold ?
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  x +   y =   90,   (1)   ( x is the number of students' tickets )
40x + 75y = 4650.   (2)   ( y is what?)

Multiply the first equation by 40 (both sides). You will get an equivalent system

40x + 40y = 3600,   (1')
40x + 75y = 4650.   (2')

Now distract equation (1') from equation (2'). You will get a single equation for y:

35y = 4650 - 3600,  or

35y = 1050.

Hence, y = 1050%2F35 = 30.

Thus the number of adults' tickets is 30.

Now find the number of students' tickets.

Solved.

The method I applied here is called the elimination method.

The substitution method is also applicable. You can do it on your own.

If you want to extend your knowledge, read the lessons
    - Solution of a linear system of two equations in two unknowns by the Substitution method
    - Solution of a linear system of two equations in two unknowns by the Elimination method
    - Solution of a linear system of two equations in two unknowns using determinant
    - Geometric interpretation of a linear system of two equations in two unknowns
    - Solving word problems using linear systems of two equations in two unknowns
in this site.


Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

For a school play, students tickets cost 40 cents and adults tickets were 75 cents .the total receipts for 90 tickets were $46.50 .how many of each kind were sold ?