A movie theater charges 8 dollars for adults and 4 dollars for seniors. On a particular day when 353 people paid an admission, the total receipts were 1688 dollars. How many who paid were adults? . How many who paid were seniors?
Answer:
There were 69 adults and 284 seniors
Solution:
Let "a" be the number of adults
Let "s" be the number of seniors
Cost of 1 adult = $ 8
Cost of 1 senior = $ 4
On a particular day when 353 people paid an admission
Therefore,
number of adults + number of seniors = 353
a + s = 353
a = 353 - s ---------- eqn 1
The total receipts were 1688 dollars
Therefore, we frame a equation as:
number of adults x Cost of 1 adult + number of seniors x Cost of 1 senior = 1688
8a + 4s = 1688 ---------- eqn 2
Let us solve eqn 1 and eqn 2
Substitute eqn 1 in eqn 2
8(353 - s) + 4s = 1688
2824 -8s + 4s = 1688
4s = 2824 - 1688
4s = 1136
s = 284
Substitute s = 284 in eqn 1
a = 353 - 284
a = 69
Thus there were 69 adults and 284 seniors in movie theater