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 produced without answering machines as 'x' and the number of phones produced with answering machines as 'y'.
According to the given information,
x + y = 600 (total number of phones produced)
y = 2x (demand for phones with answering machines is twice as great as without)
To solve this system of linear equations, we can use the substitution method.
Substitute the value of y from the second equation into the first equation:
x + 2x = 600
3x = 600
x = 600/3
x = 200
Substitute the value of x into the second equation to find y:
y = 2(200)
y = 400
Therefore, we would schedule 200 phones without answering machines and 400 phones with answering machines for production.
Let's assign some variables to represent the unknown quantities:
Let x be the number of phones without answering machines produced.
Let y be the number of phones with answering machines produced.
According to the problem, the company produces telephones at a rate of 600 per day. So we have the equation:
x + y = 600 ...(Equation 1)
The customer survey indicates that the demand for phones with answering machines is twice as great as the demand for phones without answering machines. Mathematically, this can be expressed as:
y = 2x ...(Equation 2)
We now have a system of linear equations, consisting of Equation 1 and Equation 2.
To solve this system of equations, we can use the method of substitution. We substitute the value of y from Equation 2 into Equation 1:
x + 2x = 600
Combining like terms:
3x = 600
Dividing both sides by 3:
x = 200
Now, substitute this value of x back into Equation 2 to solve for y:
y = 2x
y = 2(200)
y = 400
So, if we are deciding the production quota for the day, we would schedule 200 phones without answering machines and 400 phones with answering machines.
To solve this problem, we need to set up a system of linear equations based on the given information.
Let's denote the number of phones without answering machines as x, and the number of phones with answering machines as y.
From the first statement, we know that the company produces telephones at the rate of 600 per day, which means that the total number of phones produced can be expressed as:
x + y = 600 ----(Equation 1)
From the second statement, we know that the demand for phones with answering machines is twice as great as the demand for phones without answering machines. This can be represented as:
y = 2x ----(Equation 2)
Now, we have a system of linear equations. We can use substitution or elimination method to solve it. For this example, let's use the substitution method.
Substitute the value of y from Equation 2 into Equation 1:
x + 2x = 600
Combine like terms:
3x = 600
Divide both sides by 3:
x = 200
Now substitute the value of x back into Equation 2 to find y:
y = 2(200)
y = 400
Therefore, the company should schedule the production of 200 phones without answering machines and 400 phones with answering machines to meet the demand.