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.

honesty mood

step-by-step explanation:

5x + 3y = - 4

step-by-step explanation:

the equation of a line in standard form is

ax + by = c ( a is a positive integer and b, c are integers )

express the line first of all in slope- intercept form

y = mx + c ( m is the slope and c the y-intercept )

to calculate m use the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (7, - 3) and (x₂, y₂ ) = (4, - 8)

m = = -

y = - x + c ← is the partial equation

to find c substitute either of the 2 points into the partial equation

using (4, - 8 ), then

- 8 = - + c ⇒ c = -

y = - x - ← in slope-intercept form

multiply all terms by 3 to eliminate the fractions

3y = - 5x - 4 ( add 5x to both sides )

5x + 3y = - 4 ← in standard form