The Family Fine Arts Center charges $21 per adult and $13 per senior citizen for its performances. On a recent weekend evening when 535 people paid admission, the total receipts were $8355. How many who paid were senior citizens?

I am struggling with the right formula to use.

Do I use an arthimetic or geometric sequence?

Question

Mathematics

Isabel

10 December, 20:51

The Family Fine Arts Center charges $21 per adult and $13 per senior citizen for its performances. On a recent weekend evening when 535 people paid admission, the total receipts were $8355. How many who paid were senior citizens?

I am struggling with the right formula to use.

Do I use an arthimetic or geometric sequence?

+5

Answers (1)

Know the Answer?

Desmond Rush · Answer 1

175 adults

360 senior citizens

Step-by-step explanation:

Let x be the number of senior citizens

There were a total of 535 people, so

(535-x) = total number of adults

Total receipts=$8,355

Adult payments+Senior payments=$8,355

21 (535-x) + 13x=$8,355

$11,235-21x+13x=$8,355

$11,235-8x=$8,355

-8x=$-2,880

x=360 senior citizens

Number of adults=535-360=175 adults

To check, just substitute ...

21 (175) + 13 (360)

3,675+4,680

Which equals ...

$8,355