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a play is performed for a crowd of 400 people.adult ticket cost $22 each, student tickets cost $15 each,and tickets for children cost $13.50 each.the revenue for the concert is $7840.there are 40 more children at the concert than students.how many of each type of ticket are sold?

1 Answer

1 vote

For this case we have the following variables:

A: Represents the number of adults

S: Represents the number of students

C: Represents the number of children

For the income we have:


22A + 15S + 13.50C = 7840 -----> (1)

Regarding the number of people at the concert we have:


A + S + C = 400 -----> (2)

If there are 40 more children than students, we have:


C = 40 + S -----> (3)

We substitute C in the second equation and it remains:


A + S + 40 + S = 400


A + 40 + 2S = 400


A + 2S = 400-40


A + 2S = 360


A = 360-2S --------> (4)

Substituting (3) and (4) in (1) we have:


22 (360-2S) + 15S + 13.50 (40 + S) = 7840


7920-44S + 15S + 540 + 13.50S = 7840


7920-7840 + 540 = 44S-15S-13.50S


620 = 15.50S


S = (620)/(15.50)


S = 40

So, there are 40 children.

Substituting S in (3) and obtaining C:


C = 40 + S


C = 40 + 40


C = 80

Substituting S in (4):


A = 360-2 (40)\\A = 360-80\\A = 280

Thus, 280 tickets of adults, 80 of children and 40 of students were sold.

Answer:

280 tickets for adults, 80 for children and 40 for students


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