find the number of sold tickets from each kind.

Question

In a party of a school,290 tickets of the party had been sold.if the selling price to the student in the school is one pound and for his guest the selling price is 3 pounds .the selling price for all sold tickets is 490 L.E

find the number of sold tickets from each kind.

Answer 1

Hi Noran, let s represent a student ticket and g represent a guest ticket. Set up two equations and solve.

 

Equation 1, number of tickets sold:

 

s + g = 290

 

Equation 2, cost of tickets sold:

 

s * 1 + g * 3 = 490

 

System of equations:

 

s +   g  = 290

s + 3g  = 490

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To solve by elimination, multiply the first equation by -1:

 

-s   -    g  =  -290

 s   + 3g  =   490

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2g = 200

 

g = 100

 

There were 100 guest tickets sold.

 

From first equation:

 

s + 100 = 290

 

s = 190

 

There were 190 student tickets sold.

 

Questions?

Answer 2

Let x = the number of student tickets sold and y = the number of guest tickets sold. We can set up a system of equations.

 

x + y = 290

 

x + 3y = 490

 

The first equation represents the total number of tickets sold. The second equation represents the total price of the tickets.

 

This system of equations can be solved by either the Elimination Method or the Substitution Method.