00:01
Hi student, here we are given a situation in which a family fine arts center charges $21 per adult and $14 per senior citizen for the performances.
00:12
And in a weekend, we got a total of $4 .93 people who paid admission for performing and the total receipts of amount was $7 ,763.
00:29
We have to find the number of senior citizens who paid for performing.
00:38
So we have to take x and y, let's say, let x be the number of adults and y be the number of senior citizens.
00:57
In that case, we have total 493 people participating or performing.
01:04
So the sum of x and y would be nothing but 493.
01:11
So the first relation we can derive from the information given is that x plus y equals 493 as the total number of people is 493 which comprises adults as well as senior citizens.
01:21
Now the second thing is the total cost or total collection is $7 ,763.
01:27
This has been from adults and senior citizens together.
01:31
Each adult will give $21 so x adults will give $21x dollars similarly $14 dollars are obtained per senior citizen since there are y senior citizens 14 y would be the amount given by senior citizen so the total would be 21x plus 14 y equals 7 ,7663 as we are given two different algebraic equations and two variables also.
02:09
We can simply solve them to get the value of x and y.
02:12
Particularly we are more interested in knowing why since the question is the number of senior citizens.
02:19
So, anyways, we can move on to solving.
02:24
In order to solve that, at least any of either x or y should have the same coefficient in both of the equations...