Solve each system of linear equation and explain any method you used:
Solve each system of linear equation and explain any method you used:
-A company produces telephones at the rate of 600 per day. A customer survey indicates that the demand for phones with built in answering machines is twice as great as the demand for phones without the machines. If you are deciding the production quota for the day, how many phones with answering machines would you schedule for production? How many without answering machines would you make?
Let's assume that the demand for phones without answering machines is x per day.
According to the customer survey, the demand for phones with answering machines is twice as great as the demand for phones without answering machines. Therefore, the demand for phones with answering machines would be 2x per day.
We know that the company produces telephones at the rate of 600 per day.
To determine the production quota for each type of phone, we need to solve the following system of equations:
x + 2x = 600
Combining like terms, we get:
3x = 600
Simplifying, we find:
x = 600/3
x = 200
So, the demand for phones without answering machines would be 200 per day.
Since the demand for phones with answering machines is twice as great, the demand for phones with answering machines would be 2 * 200 = 400 per day.
Therefore, the production quota for phones with answering machines would be 400, and for phones without answering machines would be 200.