Question

Nathan and some friends are going to the movies. At the theater, they sell a bag of popcorn for $6 and a drink for $4. How much would it cost if they bought 5 bags of popcorn and 7 drinks? How much would it cost if they bought pp bags of popcorn and dd drinks?Total cost, 5 bags of popcorn, and 7 drinks: Total cost, p bags of popcorn and d drinks:

Answer 1

The total cost for 5 bags of popcorn and 7 drinks at the prices given would be $58. To calculate the cost for an undefined number of popcorn bags and drinks, represented by pp and dd respectively, the formula used is Total Cost = (p × $6) + (d × $4).

Step-by-step explanation:

The question involves calculating the total cost for certain quantities of items, specifically popcorn and drinks at a movie theater. We are given the price of one bag of popcorn as $6 and one drink as $4.

Cost Calculation for 5 Bags of Popcorn and 7 Drinks

To find the total cost for 5 bags of popcorn and 7 drinks, we use the formula:

Total Cost = (Number of Popcorn Bags × Price per Bag) + (Number of Drinks × Price per Drink)

Plugging in the numbers:

Total Cost = (5 × $6) + (7 × $4)

Total Cost = $30 + $28

Total Cost = $58

General Cost Calculation for pp Bags of Popcorn and dd Drinks

To express this in terms of variables p for popcorn bags and d for drinks:

Total Cost = (p × $6) + (d × $4)

Answer 2

a) Since the cost of a bag of popcorn is $6 and the cost of a drink is $4,

`\begin{gathered} T=6\cdot5+7\cdot4 \\ \Rightarrow T=30+28=58 \\ \Rightarrow T=58 \end{gathered}`

Therefore, the answer to the first question is $58.

b) Substitute 5 for p and 7 for d in the expression above; therefore,

`T=6p+4d`

The total cost is given by the equation T=6p+4d, where T is in dollars, p is the number of bags of popcorn and d is the number of drinks.