Ben ordered 17 pizzas for party. He ordered 3 types...cheese, pepperoni and supreme. Cheese pizza costs $8 each, pepperoni $10 each and supreme $12 each. He spent exactly twice as much on the pepperoni pizzas as he did the cheeese. If Ben spent a total of $168 on pizzas, how many pizzas of each type did he buy?

Let the number of cheese pizzas be x

Let the number of pepperoni pizzas be y

Let the number of supreme pizzas be z

Total number of pizzas = x + y + z = 17

He spent exactly twice as much on the pepperoni pizzas as he did the cheeese

i.e. 8x = 2(10 y) Therefore x = 20y/8

Total of the money spent = 168

i.e.8x + 10y + 12z = 168

       x  +  y  +   z  =  17

Multiplying the second equation by 12

         8x + 10y + 12z = 168

         12x  + 12y+12z = 204

          -4x - 2y = - 36                      (subtracting both the equations)

         -4(20y/8)  - 2y = -36

           -10y - 2y = -36

         so, y = 3

            x = 20y/8 = 20*3/8 = 7.5

remaining is z as we know that x + y + z = 17

Therefore  z = 17 - (y+ z) = 17-10.5 = 6.5

Number of cheese = x = 7.5

Number of pepperoni = y = 3

Number of supreme = z = 6.5