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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.

Respuesta :

calculista

Answer:

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

Step-by-step 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

[tex]3x+12y+20z=46[/tex] -----> equation A

[tex]2x+20y+10z=35[/tex] -----> equation B

[tex]4x+16y=48[/tex] -----> equation C

Multiply by -2 both sides equation B

[tex]-2(2x+20y+10z)=-2(35)[/tex]

[tex]-4x-40y-20z=-70[/tex] -----> equation D

Adds equation A and equation D

[tex]3x+12y+20z=46\\-4x-40y-20z=-70\\-----------\\3x+12y-4x-40y=46-70[/tex]

[tex]-x-28y=-24[/tex] -----> equation E

we have

[tex]4x+16y=48[/tex] -----> equation C

[tex]-x-28y=-24[/tex] -----> 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

[tex]x=10, y=0.5[/tex]

Find the value of z

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

[tex]2(10)+20(0.5)+10z=35[/tex]

[tex]30+10z=35[/tex]

[tex]10z=35-30[/tex]

[tex]10z=5[/tex]

[tex]z=0.5[/tex]

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

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