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the Town Theater received $22,540.75 by selling 435 tickets to the opening night of the play. if the full price of a ticket is $6.25 and discount tickets for students and seniors are $5.25 each how many full-price tickets were sold

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Mathhisfunn101

I tried solving the problem and it didn't make sense until assuming that 22540.75 was a typo for 2540.75.

Answer:

2540.75 = 6.25x + 5.25y

435 = x + y

x = number of adult tickets

y = number of student and senior tickets

Question is asking to find x

- - - - - - - - - - - - - - - - - -

435 = x + y

2283.75 = 5.25x + 5.25y

Elimination method:

2540.75 = 6.25x + 5.25y

-(2283.75 = 5.25x + 5.25y)

257 = x

257 full priced tickets were sold.

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Answer:

Full tickets sold were 257 in count and discounted tickets were 178.

Step-by-step explanation:

Let the full tickets be = f

Let the discounted tickets be = d

Total tickets sold = 435

This can be written as :

[tex]f+d=435[/tex] or[tex]f=435-d[/tex]    .....(1)

The full price of a ticket is $6.25 and discount price is $5.25 and total earning is $2540.75.

In equation form, it can be written as :

[tex]6.25f+5.25d=2540.75[/tex]    ....(2)

Substituting the value of f in (2)

[tex]6.25(435-d)+5.25d=2540.75[/tex]  

[tex]2718.75-6.25d+5.25d=2540.75[/tex]

[tex]-1d=-178[/tex]

so , d = 178

And[tex]f+d=435[/tex]

So,[tex]f=435-178=257[/tex]

Hence, full tickets sold were 257 in count and discounted tickets were 178.

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