Extremely HARD problem I don't get it ! Help me?

Luis and Jonah are planning to order a pizza. They can choose between a coupon offer and the store special:

Coupon: $13 for a plain pizza

$1 per topping



Store Special: $11 for a plain pizza

$2 per topping



Write 2 equations and show all your work to find the number of toppings that make the two choices the same price.Extremely HARD problem I don't get it ! Help me?
Let c = the price of a pizza on the coupon offer

Let s = the price of a pizza on the store special

Let t = the number of toppings on your chosen pizza



c = 13+t %26lt;---$13 plus $1 times the number of toppings

s = 11+2t %26lt;--- $11 plus $2 times the number of toppings



You want c to equal s. Since c = 13 + t and s = 11 + 2t, if c = s, then we can also set the other side of both equations as equal......



13 + t = 11 + 2t



Subtract 11 from both sides to isolate the numerals on one side...



2 + t = 2t



Subtract t from both sides to isolate the variables on the other side...



2 = t



Therefore, when both pizzas have 2 topings, both pizzas cost the same.Extremely HARD problem I don't get it ! Help me?
13 + x = 11 + 2x



x = 2



If they order two toppings, either coupon will yield a fifteen-dollar bill. Good luck. =)Extremely HARD problem I don't get it ! Help me?
The equation for the coupon offer is:



let x = number of toppings, then

let p = total price for pizza



p = 1x + 13



Now, for the store special



p = 2x + 11



To determine the number of toppings that yield the same price, we need to solve for the x that makes both equations the same. to do this, we get:



2x + 11 = x + 13

x + 11 = 13

x = 2



So, if they get 2 toppings, they will pay the same price whether they use the coupon or get the store special. Let's check the math to see if it works:



Coupon: p = x + 13 or p = 2 + 13 = 15

Special: p = 2x + 11 or p = 2*2 + 11 = 15



The answer checks.
Make the variable "X" the number of toppings.

Then the equation becomes:



coupon pizza price = store pizza price



13 + X = 11 + 2X



Use algebra to find "X":



13 - 11 - X = 11 - 11 + 2X - X

2 = X



PROOF:



The $13 pizza with 2 $1 toppings is $15

The $11 pizza with 2 $2 toppings is $15