A small theater with 200 seats sells two kinds of tickets for a performance. Premium tickets sell for $20 each and Standard tickets sell for $15 each. At a sold-out performance, $3400 was collected in ticket sales. How many tickets of each type were sold?

p + s = 200......p = 200 - s
20p + 15s = 3400

20(200 - s) + 15s = 3400
4000 - 20s + 15s = 3400
-20s + 15s = 3400 - 4000
-5s = - 600
s = -600/-5
s = 120 <=== there were 120 standard tickets sold

p + s = 200
p + 120 = 200
p = 200 - 120
p = 80 <=== there were 80 premium tickets sold

Answer Link

topeadeniran2 topeadeniran2 · Answer 2 · 2021-09-30T12:58:38+02:00

There were 120 Premium tickets sold and 80 Standard tickets.

Let the number of premium tickets = p

Let the number of standard tickets = s

Based on the information given, the equation to solve the question will be:

p + s = 200 ...... i

20p + 15s = 3400 ...... ii

From equation i, p = 200 - s

Since 20p + 15 = 3400

20(200 - s) + 15s = 3400

4000 - 20s + 15s = 3400

Collect like terms

-20s + 15s = 3400 - 4000

-5s = -600

s = 600/5

s = 120

Since p + s = 200

p = 200 - s.

p = 200 - 120

p = 80

In conclusion, there were 120 Premium tickets sold and 80 Standard tickets

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