SOLUTION: The Family Fine Arts Center charges $21 per adult and $12 per senior citizen for its performances. On a recent weekend evening when 486 people paid admission, the total receipt

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Question 1034181: The Family Fine Arts Center charges $21 per adult and $12 per senior citizen for its performances. On a recent weekend evening when 486 people paid admission, the total receipts were $6894. How many who paid were senior citizens?
a. 208 senior citizens
b. 368 senior citizens
c. 118 senior citizens
d. 278 senior citizens
Answer by ikleyn(52781) About Me  (Show Source):
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The Family Fine Arts Center charges $21 per adult and $12 per senior citizen for its performances. On a recent weekend evening when 486 people paid admission, the total receipts were $6894. How many who paid were senior citizens?
a. 208 senior citizens
b. 368 senior citizens
c. 118 senior citizens
d. 278 senior citizens
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Answer. Option b. 368 senior citizens.

Solution. 

Let s be the number of seniors.

Then the number of adults is (486-s).

The value function is f(x) = 12*s + 21*(486-s) dollars.

Only s = 368 gives the value of $6894.

To find the answer, you actually do not need to solve the equation.