Question

Three orders are placed at a pizza shop.

Answer 1

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.

$2x+y+z=14$           ...(i)

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

$x+y+3z=15$         ...(ii)

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

$3x+y+2z=22$      ...(iii)

From (i), we get

$z=14-2x-y$        ...(iv)

Putting $z=14-2x-y$ in (ii), we get

$x+y+3(14-2x-y)=15$

$x+y+42-6x-3y=15$

$-5x-2y=15-42$

$-(5x+2y)=-27$

$5x+2y=27$            ...(v)

Putting $z=14-2x-y$ in (iii), we get

$3x+y+2(14-2x-y)=22$

$3x+y+28-4x-2y=22$

$-x-y=22-28$

$-(x+y)=-6$

$x+y=6$

Multiply both sides by 2.

$2x+2y=12$    ..(vi)

Subtracting (vi) from (v), we get

$5x+2y-2x-2y=27-12$

$3x=15$

$x=5$

Putting x=5 in (vi), we get

$2(5)+2y=12$

$10+2y=12$

$2y=12-10$

$2y=2$

$y=1$

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

$z=14-2(5)-(1)$

$z=14-10-1$

$z=3$

So, $x=5,y=1,z=3$.

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