Lesson One unusual problem to solve using system of two equations
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<H2>One unusual problem to solve using system of two equations</H2> <H3>Problem 1</H3>Three kinds of tickets are sold for a school student parent dinner: a $1.00 ticket for one adult, a $1.50 ticket for one adult and one child and $2 ticket for 2 adults and one child. Total raised was $69 and 32 children and 62 adults attended. How many of each type of ticket was sold? <B>Solution</B> <pre> Let x be the number of $1.50 tickets for 1 adults and one child. Let y be the number of $2 tickets for 2 adults and one child. Then the number of $1 tickets for single adult is (62-x-2y). Then you have these two equations: x + y = 32 (1) (counting children) 1.5x + 2y + (62-x-2y) = 69 (2) (counting money) Simplify: x + y = 32, (3) 0.5x = 69-62 = 7 (4) Simplify again: x + y = 32, (5) 0.5x = 7. (6) It is clear now from (2) that x = 2*7 = 14. Then from (1) y = 32 - x = 32 - 14 = 18. <U>Answer</U>. 14 $1.50 tickets; 18 $2 tickets; and the number of $1 tickets is 62-x-2y = 62-14-2*18 = 12. </pre> <U>The lesson to learn from this solution</U>: <pre> In standard word problems solved using systems of two equations, creating a system of equations is not a difficult task. But in this case you need to stench your mind to do it correctly . . . This is why I placed this lesson and this problem here. I wanted, most of all, to reduce the problem to 2 equations and avoid having 3 equations. And I succeeded in it. 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