Question

1.1 Each week, you order dinner for your science

| club from a local pizza restaurant. An order of three
large pizzas, 12 bread sticks, and 20 chicken wings
costs $46. An order of two large pizzas, 20 bread
sticks, and 10 chicken wings costs $35. An order of
four large pizzas and 16 bread sticks costs $48. Find
the cost of each food item.

Answer 1

The cost of each large pizza is $10

The cost of each bread sticks is $0.5

The cost of each chicken wings is $0.5

Explanation:

Let

x ----> the cost of each large pizza

y ----> the cost of each bread sticks

z ----> the cost of each chicken wings

we know that

`3x+12y+20z=46` -----> equation A

`2x+20y+10z=35` -----> equation B

`4x+16y=48` -----> equation C

Multiply by -2 both sides equation B

`-2(2x+20y+10z)=-2(35)`

`-4x-40y-20z=-70` -----> equation D

Adds equation A and equation D

`3x+12y+20z=46\\-4x-40y-20z=-70\\-----------\\3x+12y-4x-40y=46-70`

`-x-28y=-24` -----> equation E

we have

`4x+16y=48` -----> equation C

`-x-28y=-24` -----> equation E

Solve the system of equations C and E by graphing

Remember that the solution of the system of equations is the intersection point both graphs

The solution is the point (10,0.5)

see the attached figure

so

`x=10, y=0.5`

Find the value of z

substitute the value of x and the value of y in the equation B and solve for z

`2(10)+20(0.5)+10z=35`

`30+10z=35`

`10z=35-30`

`10z=5`

`z=0.5`

therefore

The cost of each large pizza is $10

The cost of each bread sticks is $0.5

The cost of each chicken wings is $0.5