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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 = = 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.