Problem 50 - Algebra 2

Question

Latonya earns a commission of \(\$ 1.75\) for each magazine subscription she sells and \(\$ 1.50\) for each newspaper subscription she sells. Her goal is to earn a total of \(\$ 525\) in commissions in the next two weeks. Write an equation that is a model for the different numbers of magazine and newspaper subscriptions that can be sold to meet the goal.

Step-by-Step Solution

Answer

The equation is \( 1.75m + 1.50n = 525 \).

Step 1: Identify Variables

Let's define the variables. Let \( m \) be the number of magazine subscriptions Latonya sells. Let \( n \) be the number of newspaper subscriptions she sells.

Step 2: Understand the Commission Per Subscription

Latonya earns \( \\(1.75 \) for each magazine subscription and \( \\)1.50 \) for each newspaper subscription.

Step 3: Formulate the Equation

To find the total commission, we multiply the number of magazine subscriptions by \( \\(1.75 \) and the number of newspaper subscriptions by \( \\)1.50 \). Therefore, the equation representing her total commission goal is: \[ 1.75m + 1.50n = 525 \] where \( 1.75m \) represents the earnings from magazine subscriptions and \( 1.50n \) represents the earnings from newspaper subscriptions.

Key Concepts

Variables

In the world of mathematics and problem-solving, variables are symbols that represent unknown values. They allow us to build and solve equations. In this exercise, we need to model Latonya's commission earnings using variables.

Let's consider:

• \( m \) as the number of magazine subscriptions sold.
• \( n \) as the number of newspaper subscriptions sold.

By assigning specific symbols to these quantities, we create a clearer picture of the problem at hand. These variables help us to set up an equation that models Latonya's commission earnings goal.

Commission Calculation

Commission calculation is a crucial component of this exercise. It involves determining how much Latonya earns based on her sales. To do this, we'll multiply the number of each type of subscription by the commission earned per subscription.

Here are the earnings per subscription for Latonya:

• \( \\(1.75 \) for each magazine subscription.
• \( \\)1.50 \) for each newspaper subscription.

To calculate the total commission, we use the formula: \( 1.75m + 1.50n \). Here, \( 1.75m \) calculates her earnings from magazines and \( 1.50n \) calculates her earnings from newspapers, helping to shape the overall understanding of her potential sales income.

Goal Setting

Goal setting is essential for both personal and professional success. In Latonya's case, her goal is to earn a certain amount in commissions. This sets a clear target for her efforts and productivity.

Latonya's commission goal is \( \$525 \). This means that, in order for her to meet her target, the total calculated commission from magazine and newspaper subscriptions should equal \( 525 \). By creating an equation, \[ 1.75m + 1.50n = 525 \], we establish a systematic approach to understanding what it will take for Latonya to reach her financial objective over the two-week period.

Subscriptions

Subscriptions are commitments from customers to regularly receive products or services. In Latonya's situation, she is selling magazine and newspaper subscriptions.

Each subscription type offers a different commission, reflecting their distinct value in her earnings equation. Magazines and newspapers might appeal to different customer needs and markets, affecting how Latonya strategizes her sales approach.

By understanding the dynamics of each subscription type and its contribution to the total commission, Latonya can focus on the most effective strategies to achieve her earning goals. This understanding of subscriptions is vital in creating the equation to model her total commission earnings.