how do i write and solve a system of linear equations for a story problem

Question

scott 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.

 

 

please show steps and appreciate your help

Answer 1

Let x = price of a plain pizza no-toppings

Let y = price per topping 

 

hence 

 

x + 3y = 15.25

x + 5y = 17.75

 

solving this system of linear equations.

 

solve for x in the 1st equation and substitute into the 2nd equation

 

x = 15.25 - 3y

 

15.25 - 3y + 5y = 17.75

2y=2.50

y=1.25

 

now substitute this value for y into either of the equations to find x the value of the plain pizza

 

x= 15.25 - 3(1.25) = 15.25 - 3.75 = 11.50

 

gives us x = 11.50 and y = 1.25

 

Answer 2

Let p = the price fo a plain pizza, and t = the cost of each topping.

p+3t = 15.25 ......(1)

p+5t = 17.75 ......(2)

(2)-(1): 2t = 2.5

t = $1.25

p = 15.25-3t = $11.50

Answer 3

Let's define a variable P_b which is the cost of a plain cheese pizza.

Let's also define another variable, P_t, the cost of each topping.

We know that P_b + 3P_t = $15.25

We also know that P_b + 5P_t = $17.25

Rewriting and combining

P_b = $15.25 - 3P_t = $17.75 - 5P_t

We now have 2 equations with only one unknown (P_t)

 

$15.25 - 3P_t = $17.75 - 5P_t

Add 5P_t to each side:

 

$15.25 + Pt(5 - 3) = $17.75

 

Subtract $15.25 from each side.

 

2P_t = $17.75 - $15.25 = $2.50

 

P_t = $1.25 (the price for each topping is $1.25)

 

The cost, then, of a basic cheese pizza with no toppings is:

 

Pb = $15.25 - 3($1.25) = $11.50

 

 

Answer 4

let x be the price of pizza without toppings

let y be the price of each topping.

 

 

x + 3y = $15.25                   eq. 1

 

x + 5y = $17.75                   eq. 2

 

use eq. 1 to solve for x:

 

x = $15.25 - 3y                    eq. 3

 

substitute above in to eq. 2

 

$15.25 - 3y + 5y = $17.75

 

$15.25 + 2y = $17.75

 

2y = $17.75 - $15.25

 

2y = $2.50

 

y = $1.25

 

let's plug in y in to eq. 3 to find x:

 

 

$15.25 - 3($1.25) = x

 

x = $15.25 - $3.75 = $11.50

 

so the price of cheese pizza is $11.50 and each topping costs $1.25

 

Answer 5

Hi R;

x is the price of a plain cheese pizza

y is the price for a topping

x+3y=15.25

x+5y=17.75

 

Let's subtract the second equation from the first.  We could do the first equation from the second.  I randomly select this arrangement...

x+3y=15.25
-(x+5y=17.75)

0-2y=-2.50

-2y=-2.50

2y=2.50

y=1.25

Each topping is 1.25.

 

Let's plug-in this value into one equation to find the value of x.  I randomly select the first equation...

x+3y=15.25
x+[3(1.25)]=15.25

x+3.75=15.25

x=11.50

 

Let's verify with the second equation...

x+5y=17.75

11.50+[5(1.25)]=17.75

11.50+6.25=17.75

17.75=17.75

It works!!!