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.