One evening 1600 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $20 for covered pavilion seats and $15 for lawn seats. Total receipts were $26,000. How many tickets of each type were sold? How many pavilion seats were sold?

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Answer 1 · 2016-11-17T22:29:06

There were 400 pavilion tickets sold and 1,200 lawn tickets sold.

Let's call the pavilion seats sold #p# and the lawn seats sold #l#. We know there was a total of 1600 concert tickets sold. Therefore:

#p + l = 1600# If we solve for #p# we get #p + l - l = 1600 - 1#

#p = 1600 - l#

We also know pavilion tickets go for $20 and lawn tickets go for $15 and the total receipts were $26000. Therefore:

#20p + 15l = 26000#

Now substituting #1600 - l# from the first equation into the second equation for #p# and solving for #l# while keeping the equation balanced gives:

#20(1600 - l) + 15l = 26000#

#32000 - 20l + 15l = 26000#

#32000 - 5l = 26000#

#32000 - 5l + 5l - 26000 = 26000 + 5l - 26000#

#6000 = 5l#

#6000/5 = (5l)/5#

#1200 = l#

Substitute #1200# for #l# in the result of the first equation to solve for #p#:

#p = 1600 - 1200#

#p = 400#