Answer:
$5
Step-by-step explanation:
Let's denote the cost of one pretzel as [tex]x[/tex] and the cost of one soda as [tex]y[/tex].
According to the given information, we can set up a system of equations based on the total cost of the pretzels and sodas for each family:
For the first family:
The total cost is $30, so we have the equation:
[tex]5x + 4y = 30[/tex]
For the second family:
The total cost is $33, so we have the equation:
[tex]4x + 5y = 33[/tex]
We now have a system of two equations:
[tex]\begin{cases} 5x + 4y = 30 \\ 4x + 5y = 33 \end{cases}[/tex]
We can solve this system using any method, such as substitution or elimination. Let's solve it using the elimination method:
Multiplying the first equation by 5 and the second equation by 4 to eliminate [tex]y[/tex], we get:
[tex]\begin{cases} 25x + 20y = 150 \\ 16x + 20y = 132 \end{cases}[/tex]
Now, we can subtract the second equation from the first:
[tex](25x + 20y) - (16x + 20y) = 150 - 132[/tex]
[tex]25x + 20y - 16x - 20y = 18[/tex]
[tex]9x = 18[/tex]
[tex] x = \dfrac{18}{9}[/tex]
[tex]x = 2[/tex]
Now that we have found the cost of one pretzel ([tex]x = 2[/tex]), we can substitute it back into one of the original equations to find the cost of one soda.
Let's use the first equation:
[tex]5(2) + 4y = 30[/tex]
[tex]10 + 4y = 30[/tex]
[tex]4y = 20[/tex]
[tex]y =\dfrac{20}{4}[/tex]
[tex]y = 5[/tex]
Therefore, the cost of one soda is $5.
