Question

Item 7 three orders are placed at a pizza shop. two small pizzas, a liter of soda, and a salad cost $14; one small pizza, a liter of soda, and three salads cost $15; and three small pizzas, a liter of soda, and two salads cost $22. how much does each item cost?

Answer 1

For this case, the first thing we must do is define variables.

We have then:d

x: cost of each small pizza

y: cost of each liter of soda

z: cost of each salad.

We write the equation that models the problem:

`2x + y + z = 14`

`x + y + 3z = 15`

`3x + y + 2z = 22`

From equation 3 we clear y:

`y = 22 - 3x -2z`

Substituting in equation 2 we have:

`x + (22 - 3x -2z) + 3z = 15`

Rewriting:

`-2x + z = -7`

From here, we clear the value of z:

`z = -7 + 2x`

Then, we substitute the value of z and y in equation 1:

`2x + (22 - 3x -2 (-7 + 2x)) + (-7 + 2x) = 14`

From here, we clear x:

`2x + (22 - 3x + 14 - 4x) + (-7 + 2x) = 14`

`2x + (36 - 7x) + (-7 + 2x) = 14`

`-3x + 29 = 14`

`-3x = 14-29`

`-3x = -15`

`x = 5`

Then, the value of z is:

`z = -7 + 2x`

`z = -7 + 2 (5)`

`z = -7 + 10`

`z = 3`

Finally, the value of y is:

`y = 22 - 3x -2z`

`y = 22 - 3 (5) -2 (3)`

`y = 22 - 15 - 6`

`y = 1`

Answer:

$ 5: cost of each small pizza

1 $: cost of each liter of soda

3 $: cost of each salad.