The Correct Answer and Explanation is:
The correct equation is m = 5d.
This problem asks us to create a mathematical equation that models a real world situation. The goal is to express the relationship between the total money Johnny earns, represented by the variable m, and the number of days he works, represented by the variable d. To build this equation, we need to identify the key pieces of information and how they relate to one another.
First, we are given a constant rate of earning: Johnny makes $5 per day. This value is a constant because it does not change regardless of how many days he works. For every single day of work, his total earnings increase by this specific amount.
Next, we identify the variables. The variable d represents the number of days, which is the independent variable because we can choose its value. The variable m represents the total amount of money earned, which is the dependent variable because its value depends directly on the number of days worked.
The relationship between these components is one of direct multiplication. To find the total earnings, we must multiply the amount earned per day by the number of days. For instance, if Johnny works for 1 day, he earns $5 × 1 = $5. If he works for 2 days, he earns $5 × 2 = $10. If he works for 10 days, he earns $5 × 10 = $50.
We can generalize this pattern into a single formula. The total money (m) is always equal to the rate ($5) multiplied by the number of days (d). In mathematics, we write this relationship as an equation.
Therefore, the equation that shows how much money, m, Johnny earns for d days is m = 5d. This simple linear equation effectively captures the relationship, allowing anyone to calculate his total earnings for any number of days.
