At the county fair, the Baxter family bought 6 hot dogs and 4 juice drinks for $15.30. The Farley family bought 3 hot dogs and 4 juice drinks for $9.75. 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

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)