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At the baseball game last weekend, the Smith, Jones, and Garcia families each bought snacks from the concession stand. The Smith family purchased 3 hot dogs, 1 drinks, and 4 pretzels for $19.50. The Jones family spent $10.00 on 2 hot dogs, 2 drinks, and a pretzel. The Garcia family bought 3 hot dogs, 2 drinks, and 2 pretzels for $15.

What is the cost of a drink?

Respuesta :

Answer:

The cost of a drink is $1.5

Step-by-step explanation:

Let x be the cost of 1 hot dog , y be the cost of 1 drink and z be the cost of 1 pretzel

We are given that The Smith family purchased 3 hot dogs, 1 drinks, and 4 pretzels for $19.50.

So, 3x+y+4z=19.50 ---1

We are also given that The Garcia family bought 3 hot dogs, 2 drinks, and 2 pretzels for $15.

So, 3x+2y+2z=15 ---2

We are also given that The Jones family spent $10.00 on 2 hot dogs, 2 drinks, and a pretzel.

2x+2y+z=10 ---3

Substitute the value of y from 1 in 2 and 3

3x+2(19.50-3x-4z)+2z=15  and 2x+2(19.50-3x-4z)+z=10

-3x-6z+24=0----4 and -4x-7z+29=0 ---- 5

Substitute the value z from 4 in 5

[tex]-4x-7(\frac{-24+3x}{-6})+29=0[/tex]

x=2

Substitute the value of x in 4

-3(2)-6z+24=0

z=3

Substitute the value of x and z in 1

3(2)+y+4(3)=19.50

y=1.5

Hence the cost of a drink is $1.5

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