Question

As shown in Exhibit \(11,\) the \(\$ 1\) per pack sales tax on cigarettes raises tax revenue per day totaling: a. \(\$ 5\) million. b. \(\$ 6\) million. c. \(\$ 10\) million. d. \(\$ 15\) million.

Short answer

The solution cannot be determined without more information about the number of packs of cigarettes sold per day. Additional data is needed to calculate the correct tax revenue.

Step-by-step solution

Identify the variable

In this situation, the variable we need to find is the number of cigarette packs sold per day. Let's denote this variable as P.

Write the equation for total tax revenue

Since the tax is \(1 per pack, the total tax revenue per day, R, can be expressed as the product of the number of packs sold per day (P) and the tax per pack (\)1): R = P * $1

Analyze the provided options

To find the correct answer, we will consider each of the provided options and multiply them by one million. If the result makes sense in the context of the calculation, then the answer is correct. a. \(5 \textrm{ million}: 5 * \$1 = \$5\textrm{ million: This suggests that} P = 5\textrm{ million packs.}\) b. \(6 \textrm{ million}: 6 * \$1 = \$6\textrm{ million: This suggests that} P = 6\textrm{ million packs.}\) c. \(10 \textrm{ million}: 10 * \$1 = \$10\textrm{ million: This suggests that} P = 10\textrm{ million packs.}\) d. \(15 \textrm{ million}: 15 * \$1 = \$15\textrm{ million: This suggests that} P = 15\textrm{ million packs.}\) In this case, since there is no provided data to invalidate any of these options, we cannot determine the correct answer without more information. Therefore, we need additional data regarding the number of packs sold per day to identify the correct tax revenue.

Key concepts

Sales Tax

Sales tax is a consumption tax imposed by the government on the sale of goods and services. When you buy an item, sales tax is added to the item’s price. The total amount you pay includes the original price plus the sales tax. For instance, if the sales tax is set at a certain rate per item, such as \(1 per pack of cigarettes, this fixed amount is multiplied by the number of items sold to calculate the total tax collected.

Understanding how sales tax works is crucial for both consumers and businesses. Consumers need to know how much extra they are paying, whereas businesses must collect the correct amount of tax and pass it on to the government. Misunderstanding or misapplying sales tax can lead to serious financial discrepancies. That's why, in our exercise, it's essential to multiply the \)1 sales tax per pack of cigarettes by the total number of packs sold to find the total tax revenue.

Variable Identification

Variable identification is the process of determining the unknown quantities that we need to find in order to solve a problem. When tackling mathematical problems, especially those pertaining to tax calculations, identifying the correct variable is critical. In the exercise, the variable 'P' represents the number of cigarette packs sold per day.

Identifying this variable allows us to set up an equation to find the total tax revenue. Properly identifying variables in any equation is akin to finding the right pieces in a puzzle; without the correct pieces, you cannot complete the picture. Hence, problems with multiple-choice options typically test your ability to infer variables and apply them in calculations.

Equation for Total Tax Revenue

The equation for total tax revenue is a simple yet powerful tool to calculate how much money the government earns from taxes on sales. The general form of the equation is:
R = P \times T
where R represents the total tax revenue, P is the quantity of products sold, and T is the tax imposed on each product.

For the given exercise, where the sales tax on each pack of cigarettes is \(1, the equation simplifies to R = P \times \)1. This implies that the total tax revenue is directly equal to the number of packs sold. To apply this equation, we test each option from the multiple-choice question by replacing 'P' in the equation with the value represented by each option. The correct tax revenue would be a logical estimate of the number of packs sold if we had additional data on cigarette sales.

The ease of calculating total tax revenue using such a straightforward equation underlines the importance of the underlying concepts. By understanding variable identification and the role of sales tax, we can use the equation to solve real-world taxation problems effectively.