# $ 8 for adults & $ 5 for seniors. 325 people paid, the total receipts were $ 2569. How many paid were adults? How many paid were seniors? // //

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### 3 Answers

Let us assume that the number os adults = x

And assume that the number os seniors = y

We are given that total people paid is 325.

==> x + y = 325

==> x= 325 - y ...........(1)

We are given that :

cost for an adults = 8

==> total cost for adults = cost per adult * total number of adults

= 8*x

Cost for a senior = 5

==> total cost for seniors = 5*y

But total cost ( adults and seniors) = 2569

==> 8x + 5y = 2569 .........(2)

From (1), we will substitute in (2):

==> 8(325-y) + 5y = 2569

==> 2600 - 8y + 5y = 2569

==> 2600 - 3y = 2569

==> 3y = 31

==> y= 31/3 = 10.33 which is impossible because number of seniors should be an integer.

We will assume that y= 10 and total cost where 2570

==>** total number of seniors = 10**

** total number of adults = 315.**

This problem can be solved in the following way using the information provided.

The total number of people who paid: 325

Let the number of adults be A

The number of seniors = 325 - A

The amount paid by one adult was $8, So the total collection from the adults is 8A

The amount paid by one senior was $5, so the total collection from the seniors is (325 - A )*5

As the total collection is 2569 we have

8A + (325 - A )*5 = 2569

=> 8A + 1625 - 5A = 2569

=> 3A = 2569 - 1625

=> 3A = 944

=> A = 944 / 3

As 944 / 3 is not an integer but A which is the number of adults has to be an integer, there is an error in the information provided. It is not possible to find the number of seniors and number of adults.

Let a be the number of adults s be the number of seniors.

The amount paid by a number of adults @ $8 per person = 8a

The amount paid by the s sinior @ 5 per person = 5s.

The total amouny paid by (a+s = 325) persons = (8a+5s) = 2569

So the required equation is setup.

a+s = 325..........(1)

(28a+5s = 2569.........(2)

(2)- 5*(1) gives: (8a+5s) -5(a+s) = 2569-5*325

3a = 944

a =944/3 = 314.4...

Similarly ,

Eq(2) -8*Eq(1) gives: (8a+5s)-8*(a+s) = -3s = -31

So s = -31/-3 = 10.33..

The fractional solution is emberassing.

**So we suggest the total bill collection to be $2569 +$1 = $2570**

**Then a = 315 and b = 10 and a+b = 315+10 = 325.**

**And the recieved amount = 315*8+10*5 = $2570.**