## 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 dis

Question

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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1 week 2021-09-15T01:39:32+00:00 2 Answers 0

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 :

or    …..(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 :

….(2)

Substituting the value of f in (2)

so , d = 178

And

So,

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

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

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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