Question

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?

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.