5. 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 the number of phones without answering machines produced per day is x, and the number of phones with answering machines produced per day is y.
According to the problem, the company produces 600 phones per day, so we can create the first equation:
x + y = 600 (Equation 1)
The demand for phones with answering machines is twice as great as the demand for phones without answering machines. We can represent this by the equation:
y = 2x (Equation 2)
To solve this system of linear equations, we'll use the substitution method, where we solve one equation for one variable and substitute it into the other equation.
From Equation 2, we can solve for y:
y = 2x
Now, we substitute this value of y in Equation 1:
x + 2x = 600
3x = 600
Dividing both sides by 3, we get:
x = 200
Now that we have the value of x, we can substitute it back into Equation 2 to find y:
y = 2x
y = 2(200)
y = 400
So, the company should schedule 200 phones without answering machines and 400 phones with answering machines for production.
To solve this problem, we can use a system of linear equations. Let's denote the number of phones without answering machines as x, and the number of phones with answering machines as y.
1. The company produces telephones at a rate of 600 per day, so the total number of phones produced should be equal to 600:
x + y = 600
2. The customer survey indicates that the demand for phones with answering machines is twice as great as the demand for phones without answering machines. This gives us the equation:
y = 2x
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the substitution method:
From equation 2, we know that y = 2x. Substitute this into equation 1:
x + 2x = 600
3x = 600
x = 200
Now we can calculate the value of y using equation 2:
y = 2 * 200
y = 400
Therefore, to meet the production quota for the day, we should schedule 200 phones without answering machines and 400 phones with answering machines.
Let's denote the number of phones without answering machines as x, and the number of phones with answering machines as y.
According to the given information, the demand for phones with answering machines is twice as great as the demand for phones without answering machines. In other words, y = 2x.
Also, the company produces telephones at the rate of 600 per day, so the total number of phones produced should be the sum of phones with and without answering machines. Therefore, x + y = 600.
Now, we have a system of equations:
y = 2x,
x + y = 600.
To solve this system, we can use the method of substitution. Rearrange the first equation to solve for y in terms of x:
y = 2x.
Substitute this value of y into the second equation:
x + 2x = 600,
3x = 600,
x = 200.
Now, substitute this value of x into the first equation to find y:
y = 2(200),
y = 400.
Therefore, you should schedule 200 phones without answering machines and 400 phones with answering machines for production.