At the county fair, the baxter family bought 6 hot dogs and 4 juice drinks for $14.70. the farley family bought 3 hot dogs and 4 juice drinks for $9.45. find the price of a hot dog and the price of a juice drink.

A hot dog would cost 1.75 and the juice would cost 1.05

Step-by-step explanation:

In order to find this, set x as the number of hot dogs and y as the number of juice drinks. This allows us to set up the following equations for each situation.

6x + 4y = 14.70

3x + 4y = 9.45

Now we can mutliply the second equation by -2 to get the x values to cancel out.

6x + 4y = 14.70

-6x - 8y = -18.90

-4y = -4.20

y = 1.05

Now that we have this, we can plug it into either equation to find the cost of a hot dog.

3x + 4y = 9.45

3x + 4(1.05) = 9.45

3x + 4.20 = 9.45

3x = 5.25

x = 1.75