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 below)However, if A is charged with the price of C and C is...

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 below)

However, if A is charged with the price of C and C is charged with the price of A, the total bill will be increased by $450. How many A, B, C were served by the resto?

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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.

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