Answer:
Each hotdog costs $1.65
Each juice drink costs $1.05
Step-by-step explanation:
Let's begin by letting [tex]x[/tex] represent the number of hot dogs and [tex]y[/tex] the number of juice drinks.
The Baxter family bought 6 hot dogs and 4 juices for $14.10.
[tex]6x + 4y = 14.10[/tex]
The Farley family bought 3 hot dogs and 4 juices for $9.15.
[tex]3x + 4y = 9.15[/tex]
Now, we subtract these equations.
[tex]6x + 4y = 14.10\\- (3x + 4y = 9.15)[/tex]
Since [tex]y[/tex] has reversed coefficients, it gets eliminated. Now solve for x.
[tex]6x+4y-3x-4y=14.1-9.15\\3x = 4.95\\\frac{3x}{3} = \frac{4.95}{3}[/tex]
[tex]\frac{4.95}{3} = 1.65[/tex]
[tex]x = 1.65[/tex]
NOW, we find y by substituting x with 1.65 (in either equation).
We'll use the first equation.
[tex]6x + 4y = 14.10[/tex]
[tex]6(1.65) + 4y = 14.10[/tex]
[tex]9.9 + 4y = 14.10\\4y = 14.1 - 9.9\\4y = 4.2[/tex]
[tex]\frac{4y}{4} = \frac{4.2}{4} \\y = 1.05[/tex]
[tex]x[/tex] = 1.65
[tex]y[/tex] = 1.05
[tex]x[/tex] represents hotdogs and [tex]y[/tex] represents juice drinks.
Therefore, each hotdog costs $1.65 and each juice drink costs $1.05.
I hope this helps! :)
