Question

Dan, John, and Wayne have a total of 3000 stocks in a certain company. Wayne has the most stocks, and Dan has the least. Wayne has 75 more stocks than 4 times what Dan has. The difference between what Dan and John have is 125.

What system of equations represents this scenario?

Answer 1

To represent this scenario, we can create a system of equations using the given information. By solving this system of equations, we can find the values of x, y, and z, which represent the number of stocks each person has.

Step-by-step explanation:

The student is asking to find a system of equations that correctly represents the given stock-holding scenario involving Dan, John, and Wayne. We need to establish variables for the amount of stock each person has, then create equations based on the information provided.

To represent this scenario, we can create a system of equations using the given information:

Let x be the number of stocks Dan has, y be the number of stocks John has, and z be the number of stocks Wayne has.

We have the following equations:

1. z = 4x + 75 (Wayne has 75 more stocks than 4 times what Dan has)
2. x + 125 = y (The difference between what Dan and John have is 125)
3. x + y + z = 3000 (Dan, John, and Wayne have a total of 3000 stocks)

By solving this system of equations, we can find the values of x, y, and z, which represent the number of stocks each person has. This will provide a solution to the scenario.