i need help

Question

a tour group split into two groups when waiting in line for food at a fast food counter. The first group bought 8 slices of pizza and 6 soft drinks for $34.78. The second group bought 6 slices of pizza and 5 soft drinks for $26.91. How much does one slice of pizza cost?

Answer 1

Let x = price of a slice of pizza

     y = price of a soft drink

 

Then 8x + 6y = 34.78

        6x + 5y = 26.91

 

Solve the system by the elimination method:

 

       Multiply the first equation by 5 and the  second equation by -6:

 

          40x + 30y =  173.90

         -36x -  30y = -161.46

 

       Adding the equations, we get:  4x = 12.44

 

                                             So, x = $3.11

 

        Substitute for x into one of the original equations to obtain:

 

            8(3.11) + 6y = 34.78

 

                          6y = 9.9

 

                           y = $1.65

 

A slice of pizza costs $3.11 and a drink costs $1.65.

 

 

 

 

                

Answer 2

In this situation you have two equations and two unknowns. Set them up like this:

 

8p + 6d = 34.78

6p + 5d = 26.91

 

Where p is pizza slices and d is drinks.

 

Choose one of the equations and solve for d. I will use the first one.

 

8*p+6*d=34.78

6*d=-8*p+34.78

d=1/6*(-8*p+34.78)

 

d=-4/3*p+5.7967

 

You can then substitute that value into the second equation.

 

6*p+5*s=26.91

6*p+5*(-4/3*p+5.7967)=26.91

 

Solve for p

 

-2/3*p+28.983=26.91

 

p=3.11

 

Each slice of pizza costs 3.11.