SOLUTION: A small town is hosting a play as a fundraising project for a family in the town. Individuals may purchase tickets for $26 each. As a special incentive to attract couples, indivi

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Question 38777: A small town is hosting a play as a fundraising project for a family in the town. Individuals may purchase tickets for $26 each. As a special incentive to attract couples, individuals may purchase a "couple package" for $32. (note: the "couple package" allows 2 people to attend the play for the price of $32.) On the first day of sales 23 tickets were sold and $694 was collected. How many tickets were sold to individuals for $26 each? How many people were convinced to buy the "couple package"?
Answer by Nate(3500) About Me  (Show Source):
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A small town is hosting a play as a fundraising project for a family in the town. Individuals may purchase tickets for $26 each. As a special incentive to attract couples, individuals may purchase a "couple package" for $32. (note: the "couple package" allows 2 people to attend the play for the price of $32.) On the first day of sales 23 tickets were sold and $694 was collected. How many tickets were sold to individuals for $26 each? How many people were convinced to buy the "couple package"?
Define variables:
i=number of individual's tickets
c=number of couple's tickets
Define equations:
i+%2B+c+=+23
26i+%2B+32c+=+694
Combine:
-26i+-+26c+=+-598
+
26i+%2B+32c+=+694
=
+6c+=+96+
++c+=+16+
Plug in:
i+%2B+c+=+23
i+%2B+16=+23
i+=+7