Question

1. A large cheese pizza at Joe’s Pizzeria costs $0.25 for each topping plus a flat fee of $10.00. The cost of a large cheese pizza at Sam’s Pizza is $0.50 for each topping plus a flat fee $8.00. Write a system of equations to represent this situation and then determine how many toppings need to be added to a large cheese pizza from Joe’s Pizzeria and Sam’s Pizza in order for the pizzas to cost the same, not including tax. 8 toppings 1.5 toppings 4 toppings 12 toppings

Answer 1

y=total amount of money

x=# of toppings

At JOES PIZZA

Large cheese- $0.25 per topping + base fee of $10

equation- y=0.25x+10

At SAMS PIZZA

Large Cheese- $0.50 per topping + base fee of $8

equation- y=0.5x+8

SYSTEM OF EQUATIONS

y=0.25x+10

y=0.5x+8

lets try 8 toppings first

y=0.25(8)+10

y=2+10

y=12

y=0.5(8)+10

y=4+10

y=14

8 does not work

lets try 1.5 topppings next

y=0.25(1.5)+10

y=0.375+10

y=10.375

y=0.5(1.5)+8

y=0.75+8

y=8.75

1.5 does not work

lets try 4 toppings next

y=0.25(4)+10

y=1+10

y=11

y=0.5(4)+8

y=2+8

y=10

4 does not work

finally 12 must work

y=0.25(12)+8

y=3+8

y=11

y=0.5(12)+8

y=6+8

y=14

we got y=11 for the first equation with 12 toppings y=11 for the first equation with 4 toppings

12+4=18

12 toppings at joes and 4 at sams i believe