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

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

12 servings. 4 times 3= 12

answer: e 9, 5.75

step-by-step explanation:

step 1

find the variation ab in the x coordinate

delta x=(x2-x1)=10-> 8 units

find the variation ab  in the y coordinate 

delta y=(y2-y1)=6-> 2 units

step 2

find the coordinates point c

  x coordinate 

cx=ax+delta x*2/> cx=2+8*(2/> cx=3

  y coordinate 

cy=ay+delta y*2/> cy=4+2*(2/> cy=4.25

the coordinates of point c are (3,4.25)

step 3

find the coordinates point d

  x  coordinate 

dx=ax+delta x*4/> dx=2+8*(4/> dx=4

  y  coordinate 

dy=ay+delta y*4/> dy=4+2*(4/> dy=4.5

the coordinates of point d are (4, 4.5)

step 4

find the coordinates point e

  x  coordinate 

ex=ax+delta x*4/> ex=2+8*(6/> ex=5

  y  coordinate 

ey=ay+delta y*4/> ey=4+2*(6/> ey=4.75

the coordinates of point e are (5, 4.75)

step 5

find the coordinates point f

  x  coordinate 

fx=ax+delta x*4/> fx=2+8*(8/> fx=6

  y  coordinate 

fy=ay+delta y*4/> fy=4+2*(8/> fy=5

the coordinates of point f are (6,5)

step 6

find the coordinates point g

  x  coordinate 

gx=ax+delta x*4/> gx=2+8*(10/> gx=7

  y  coordinate 

gy=ay+delta y*4/> gy=4+2*(10/> gy=5.25

the coordinates of point g are (7,5.25)

step 7

find the coordinates point h

  x  coordinate 

hx=ax+delta x*4/> hx=2+8*(12/> hx=8

  y  coordinate 

hy=ay+delta y*4/> hy=4+2*(12/> hy=5.5

the coordinates of point h are (8,5.5)

step 8

find the coordinates point i

  x  coordinate 

ix=ax+delta x*4/> ix=2+8*(14/> ix=9

  y  coordinate 

iy=ay+delta y*4/> iy=4+2*(14/> iy=5.75

the coordinates of point i are (9,5.75)

- r3ktforgood ☕