Three orders are placed at a pizza shop. two small pizzas, a liter of soda, and a salad cost $28; one small pizza, a liter of soda, and three salads cost $30

Question

and three small pizzas, a liter of soda, and two salads cost $44. How much does each item cost ?

Pizza: $

Liter of Soda: $

Salad: $

Answer 1

Hi Izabel G.,

this is a classic 3-equations in 3-unknowns problem. Transform the data into equations, using x, y, and z to represent the costs of each of the items individually, then solve the equations by elimination.

-- Cheers, --Mr. d.

Answer 2

Let x = cost of pizza, y = cost of one liter of soda, and z = cost of salad. Then we have the following equations:

2x + y + z = 28

x + y + 3z = 30

3x + y + 2z = 44

We will use the elimination method to solve for each variable.

1.) Multiply the 2nd equation by -1 and add it to the 1st equation.

2x + y + z = 28

-x - y - 3z = -30

x - 2z = -2

2.) Multiply the 3rd equation by -1 and add it to the 1st equation.

2x + y + z = 28

-3x - y - 2z = -44

-x - z = -16

3.) Add both equations to find z.

x - 2z = -2

-x - z = -16

-3z = -18

z = 6

4.) Substitute the value to one of the newer equations to find x.

x - 2(6) = -2 ⇒ x - 12 = -2 ⇒ x = 10

5.) Substitute both values to one of the original equations to find y.

2(10) + y + 6 = 28 ⇒ 20 + y + 6 = 28 ⇒ 26 + y = 28 ⇒ y = 2

The cost of one small pizza is $10. The cost of one liter of soda is $2. The cost of one salad is $6.

Answer 3

set up three equations using first letter of items.

p-pizza

l- litre

s-salad

2p+l+s=28

2p+l+3s=30

3p+l+2s=44

you already have 3 equations.