Question

A concert promoter needs to make $60,600 from the sale of 1720 tickets. The promoter charges $30 for some tickets and $45 for the others. Let x represent the number of $30 tickets and y represent the number of $45 tickets. (a) Write an equation that states that the sum of the tickets sold is 1720. (b) Write an expression for how much money is received from the sale of $30 tickets? $ (c) Write an expression for how much money is received from the sale of $45 tickets? $ (d) Write an equation that states that the total amount received from the sale is $60,600. (e) Solve the equations simultaneously to find how many tickets of each type must be sold to yield the $60,600. x = y =

Answer 1

a) x +y = 1720

b) 30x

c) 45y

d) 30x +45y = 60600

e) (x, y) = (1120, 600)

Explanation:

The variables are defined for you. All you need to do is realize that the revenue from some number of tickets is the product of their price and the number of them.

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a)

x + y = 1720 . . . . . the total number of tickets sold is 1720

__

b)

30x . . . . . . . . . . . revenue from sale of $30 tickets

__

c)

45y . . . . . . . . . . revenue from sale of $45 tickets

__

d)

30x +45y = 60,600 . . . . . . total revenue is 60,600

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e)

We can use the first equation to write an expression for x that can be substituted into the second equation.

x = 1720 -y

30(1720 -y) +45y = 60,600

51600 +15y = 60600 . . . . . . . . . eliminate parentheses, collect terms

15y = 9000 . . . . . . . . . . . . . . . subtract 51600

y = 600 . . . . . . . . . . . . . . . . divide by 15

x = 1720 -600 = 1120

The number of tickets that must be sold is ...

x = 1120

y = 600