A resto agreed to serve snack to 100 people charged per person is $5 for A, $10 for B & $20 for C. The total bill is $975. (continued...

There are three kinds of snacks served, A for $5, B for
$10 and C for $20.

Let the number of people who took A be
a, those that took B be b and those that took C be c.

As
the total number of people served is 100, a + b + c = 100
...(1)

The total bill is: 5a + 10b + 20c = 975
...(2)

If the charge of A and C are interchanged, the bill
increased by $450, this gives: 20a + 10b + 5c = 975 + 450 = 1425
...(3)

(3) - (2)

=> 15a
- 15c = 450

=> a - c =
30

=> a = 30 +
c

substitute in (1)

=>
30 + c + b + c = 100

=> 2c + b =
70

=> b = 70 -
2c

Substitute a and b in
(2)

=> 5(30 + c) + 10(70 - 2c) + 20c =
975

=> 150 + 5c + 700 - 20c + 20c =
975

=> 5c =
125

=> c = 25

a =
55

b = 20

The bill when a =
55, b = 20 and c = 25 are substituted is 5*55 + 10*20 + 20*25 =
975

On reversing the charge for A and C, the bill is 20*55
+ 10*20 + 5*25 = 1425 which is 450 more than
975

The number of people that took A is 55,
those that took B is 20 and 25 people took C.