Problem 57 - Elementary Algebra

Question

If a calculator is sold for \(\$ 14.95,\) then the revenue in dollars, \(R,\) generated by this item is given by the formula \(R=14.95 q\), where \(q\) represents the number of calculators sold. Use the formula to determine the revenue generated by this item if 35 calculators are sold.

Step-by-Step Solution

Answer

The revenue is $523.25.

Step 1: Identify Known Values

From the problem, we know the price per calculator, which is \(14.95\), and the number of calculators sold, \(q = 35\). These are our known variables.

Step 2: Substitute Values into Formula

The revenue formula given is \(R = 14.95q\). Substituting the known value of \(q = 35\) into the formula, we have \(R = 14.95 \times 35\).

Step 3: Calculate the Revenue

Now perform the multiplication: \(14.95 \times 35 = 523.25\). Thus, the revenue generated is \(523.25\) dollars.

Key Concepts

Revenue Calculation

Calculating revenue involves understanding how much money is earned from selling certain quantities of an item. In our case, the item is a calculator and its price is fixed at \(14.95 each. Revenue is a key concept when assessing financial success.

• First, you need to determine the price of one unit, which in our case is \)14.95.
• Next, know the quantity sold, which is represented by the variable \(q\).
• Finally, multiply these two numbers to calculate the total revenue.

The formula to find the revenue \(R\) is usually given by \(R = \, (\text{price per unit}) \, \times \, (\text{quantity sold})\). By following these steps, you can easily determine how much money a business has made from selling products.

Known Values Substitution

In mathematics and algebra, substituting known values into a formula is a simple yet crucial skill. It allows you to use a general formula with specific numbers you're given.Consider the formula for revenue, \(R = 14.95q\), where \(R\) is the revenue and \(q\) is the number of calculators sold. From the exercise, we know \(q = 35\).

• Start by identifying the known values from the problem statement: price per calculator is $14.95 and \(q = 35\).
• Replace \(q\) in the formula with the known value, resulting in \(R = 14.95 \times 35\).

Being methodical about substitution helps avoid errors and ensures the mathematical expression remains valid. Whenever you substitute, check that you've inserted each known value correctly.

Multiplication of Decimals

Multiplying decimals can seem tricky at first, but with practice, it becomes straightforward. Let's break it down using the formula \(R = 14.95 \times 35\).Here's how to handle this multiplication step-by-step:

• Ignore the decimal point initially, and multiply the numbers like integers: \(1495 \times 35\).
• Calculate the product normally: \(1495 \times 35 = 52325\).
• Count the decimal places in the original numbers (two in 14.95).
• Work backwards from the right of the product, placing the decimal, which gives you 523.25.

Multiplying decimals involves practice, but when you follow these steps and keep the placement of the decimal point in mind, it becomes much easier to navigate through these calculations accurately.