Final answer:
To find the cost of a tub of popcorn, set up the equation 4(x - 3.50) + 2x = 32.50. Solve the equation by combining like terms and isolating the variable. The cost of a tub of popcorn is $7.75.
Step-by-step explanation:
To solve this problem, we can define a variable for the cost of one tub of popcorn. Let's call this variable 'x'.
According to the information given, each drink costs $3.50 less than a tub of popcorn. So, the cost of one drink can be written as 'x - 3.50'.
We also know that Tony and his friends bought 4 drinks and 2 tubs of popcorn for a total cost of $32.50. Using this information, we can set up the equation: 4(x - 3.50) + 2x = 32.50.
To find the cost of a tub of popcorn, we can solve this equation.
b. To solve the equation, we first distribute 4 to x and -3.50: 4x - 14 + 2x = 32.50.
Combining like terms, we have 6x - 14 = 32.50.
Next, we add 14 to both sides of the equation to isolate the variable: 6x = 46.50.
Finally, we divide both sides of the equation by 6 to solve for x, which represents the cost of a tub of popcorn: x = 7.75.
Therefore, the cost of a tub of popcorn is $7.75.