Three orders are placed at a pizza shop. two small pizzas, a liter of soda, and a salad costs $14.
one small pizza, a liter of soda, and three salads costs $15.
three small pizzas, a liter of soda, and two salads costs $22.
how much does each item cost?

Given:

Two small pizzas, a liter of soda, and a salad costs $14.

One small pizza, a liter of soda, and three salads costs $15.

Three small pizzas, a liter of soda, and two salads costs $22.

To find:

The cost of each item.

Solution:

Let x be the cost of a small pizza.

y be the cost of a liter of soda

z be the cost of a salad.

According to the question, two small pizzas, a liter of soda, and a salad costs $14.

          ...(i)

One small pizza, a liter of soda, and three salads costs $15.

        ...(ii)

Three small pizzas, a liter of soda, and two salads costs $22.

     ...(iii)

From (i), we get

       ...(iv)

Putting in (ii), we get

           ...(v)

Putting in (iii), we get

Multiply both sides by 2.

   ..(vi)

Subtracting (vi) from (v), we get

Putting x=5 in (vi), we get

Putting x=5 and y=1 in (iv), we get

So, .

Therefore, the cost of a pizza is $5, cost of a liter of soda is $1 and cost of salad is $3.