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Three families bought food at a baseball game. The Davis family spent $16.50 on 3 hot dogs, 2 drinks, and 1 pretzel. The Ruiz family spent $26 on 4 hot dogs, 4 drinks, and 2 pretzels. the Cho family spent $13.75 on 2 hot dogs, 1 drink, and 3 pretzels. What is the price of one pretzel?

Respuesta :

isyllus

Answer:

Price of one pretzel = $1.5

Step-by-step explanation:

Let the price of a hot dog = [tex]x[/tex]

Let the price of a drink = [tex]y[/tex]

Let the price of a pretzel = [tex]z[/tex]

As per the given question statement:

[tex]3x+2y+z=\$16.50..... (1)\\4x+4y+2z=\$26........ (2)\\2x+y+3z=\$13.75..... (3)[/tex]

To find:

The price of one pretzel, i.e. [tex]z=?[/tex]

Multiplying (3) with 2 and subtracting (1) from it:

[tex]x+5z=11[/tex] ..... (4)

Multiplying (3) with 4 and subtracting (2) from it:

[tex]4x+10z=29[/tex] ..... (5)

Multiplying (4) with 4 and subtracting (5) from it:

[tex]10z=15\\\Rightarrow z =\bold{1.5}[/tex]

The price of one pretzel is $1.50.

Calculation of the price:

Let the price of a hot dog = x

Let the price of a drink = y

Let the price of a pretzel = z

So,

The equations are

3x + 2y + z = $16.50 .....(1)

4x + 4y + 2z = $26..........(2)

2x + y + 3z = $13.75........(3)

Now

Here we Multiplying (3) with 2 and subtracting (1) from it:

So, it gives x + 5z = 11 ......(4)

Now

Multiplying (3) with 4 and subtracting (2) from it:

So, 4x + 10z = 29...(5)

Now

Multiplying (4) with 4 and subtracting (5) from it:

So, 10z = 15

x = 1.5

Therefore, The price of one pretzel is $1.50.

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