concession math!!!

Question

You observe 3 people making orders at the movie theater concession stand. The first person orders 2 popcorns, 1 pop, and 4 candy bars and spends $24. The second person orders 3 popcorns, 3 pops, and 1 candy bar and spends $28. The third person orders 1 popcorn, 1 pop, and 1 candy bar and spends $11. How much do popcorn, pop, and candy cost?

Answer 1

a = # of popcorns

b = # of pops

c = # of candy bars

1: 2a + b + 4c = 24

2: 3a + 3b + c = 28

3: a + b + c = 11

1) Start with Equations 2 and 3. Mulitply Eq. 3 by -1 and you get

3a + 3b + c = 28

-a - b - c = -11

2) Add them and you get 4: 2a + 2b = 17

3) Start with Equations 1 and 3. Multiply Eq. 3 by -4 and you get

2a + b + 4c = 24

-4a - 4b - 4c = -44

4) Add them and you get 5: -2a - 3b = -20

5) Use Equations 4 and 5 with elimination method to find b.

2a + 2b = 17

-2a - 3b = -20

-b = -3 b = 3

6) Use the value of b to find a from Equations 4 and 5.

2a + 2(3) = 17

2a + 6 = 17

2a = 11

a = 5.5

7) Use both the values of b and a to find c from the original system of equations.

5.5 + 3 + c = 11

8.5 + c = 11

c = 2.5

Popcorn costs $5.50, pop costs $3, and candy bar costs $2.50.

Answer 2

Let x=cost of the popcorn

Let y=cost of the pop

Let z=cost of the candy bar

The equations would be

2x+y+4z=24

3x+3y+z=28

x+y+z=11

Can you solve the system of 3 equations manually?

I used by calculator to solve, I got:

x=$5.50

y=$3.00

z=$2.50