Question

At a high school football game Jamie buys 6 hot dogs and 4 soft drinks for $13. Amy buys 3 hot dogs and 4 soft drinks for $8.50. What is the price of a hot dog?

Answer 1

x=price of a hot dog
y=price of a soft drink
We can suggest the following system of equations:

6x+4y=13
3x+4y=8.50

We solve this system of equations by reduction method.
6x+4y=13
-(3x+4y=8.5)
------------------------
3x=4.5 ⇒x=4.5/3=1.5

Answer: the price of a hot dog will be $1.5.


If you want to know the price of a soft drink, you have to find "y".
6x+4y=13

6(1.5)+4y=13
9+4y=13
4y=13-9
4y=4
y=4/4
y=1

The price of a soft drink is $1.

Answer 2

The price of a hot dog, x = $1.1 and the price of soft drink, y = $1.6

Explanation:

Let, x= price of a hot dog and y= price of a soft drink

Now, Jamie buys 6 hot dogs and 4 soft drinks for $13.

Then,
`6x+4y=13`

Also, Amy buys 3 hot dogs and 4 soft dogs for $8.50.

Then,
`3x+4y=8.5`

Thus, the system of equations is given by,

`6x+4y=13\ .........(1)\\\\3x+4y=8.5\ ...........(2)`

Multiplying (2) by 3 and subtracting the equations, we have,

`8y=12.5\\\\y=1.6`

Then, putting the value of 'y' in equation (1) gives us,

`6x+4* 1.6=13\\\\6x=13-6.4\\\\6x=6.6\\\\x=1.1`

Thus, the price of a hot dog, x = $1.1 and the price of soft drink, y = $1.6