How to solve this problem

Question

Christopher orders a 3 topping pizza for $15.25, and a 5 topping pizza for $17.75. Write and solve a system of linear equations to find the price of a plain cheese pizza (no toppings) and the cost of each topping.

Answer 1

Hello Hannah,

 

The following is a breakdown of how to solve this equation.

 

English:

Create 2 equations that represent both situations by first establishing the variables.

 

Math:

t = cost of each topping

p = cost of cheese pizza

 

3t + p = 15.25

5t + p = 17.75

 

English:

I will solve this system by process of elimination. I have to multiply the first equation by 5 and the second equation by 3

 

Math:

5(3t + p) = 5(15.25) ---> 15t + 5p = 76.25

3(5t + p) = 3(17.75) ---> 15t + 3p = 53.25

 

English:

Subtract the two equations and solve for p.

 

Math:

   15t + 5p = 76.25

-  15t + 3p = 53.25

------------------------

            2p = 23.00

            ---    -------

             2       2

 

             p = 11.50

 

English: Substitute p = 11.50 into the first original equation and solve for t.

 

Math:

3t +  11.50 =  15.25

       -11.50   -11.50

 ----------------------

3t = 3.75

---   -----

3      3

 

t = 1.25

 

English: Put p = 11.50 and t = 1.25 into second original equation and evaluate in order to check

 

Math:

5(1.25) + 11.50 = 17.75

6.25 + 11.50 = 17.75

17.75 = 17.75

 

English: Write Answer

 

A Cheese Pizza costs $11.50 and each topping costs $1.25.

 

Answer 2

For this problem, let P=price of the pizza and T=price for one topping.

 

The first pizza has 3 toppings and cost $15.25 (P+3T=15.25) and the second pizza has 5 toppings and cost $17.75 (P+5T=17.75).  These are the two equations you need.

 

P+3T=15.25

P+5T=17.75

 

To solve by elimination, I multiplied the first equation by -1, added the new equation to the second pizza equation to eliminate the variable P, then solved for T.

 

[P+3T=15.25]-1=-P-3T=-15.25

 

 P+5T=17.75

-P-3T=15.25

    2T=2.50

T=1.25  - This is the cost per topping.

 

Referring back to the original equations, a 3 topping pizza costs 15.25.

P+3(1.25)=15.25

P+3.75=15.25

P+3.75-3.75=15.25-3.75

P=11.50

 

I hope this helps.  If not, please feel free to contact me here on WyzAnt.

Norman M.

Answer 3

So let p = the cost of a pizza and t = the cost of one topping. Your 2 pizzas can be represented as

 

p + 3t = 15.25

p + 5t = 17.75

 

Rather than subtracting these, I usually teach students to multiply on by -1 and add....it leads to fewer mistakes!!!! So

 

-p - 3t = -15.25

 p + 5t = 17.75     add them to get

 

       2t = 2.50

         t = 1.25

 

Substitute back in either original equation and solve for p

 

p + 3(1.25) = 15.25

p + 3.75 = 15.25

p           =    11.50

 

Hope this helped.

Answer 4

The first thing to do is to set up variables.  Since they want to know the price s a plain pizza and the price of each topping, it makes sense to set up a variable for each of those.

 

So let x be the price of a plain pizza, and let y be the cost of each topping.

 

So the cost of the 3 topping pizza would be x + 3y and we know that's 15.25.  So the first equation is:

 

x + 3y = 15.25

 

Similarly, the cost of the 5 topping pizza would be x + 5y, and that's 17.75, so the second equation is:

 

x + 5y = 17.75

 

So to solve these:

 

x + 3y = 15.25

x + 5y = 17.75

 

...the easiest thing looks to be subtracting the first equation from the second:

 

2y = 2.50

 

Divide both sides by 2:

y = 1.25

 

Now plug this value for y into one of the equations, say the first:

x + 3y = 15.25

x + 3 * 1.25 = 15.25

x + 3.75 = 15.25

x = 11.50

 

So the price of a plain pizza is $11.50, and the price of each topping is $1.25