the charge c of a telephone company is partly constant and partly varies as the number of units called u,the cost of 50 units is 2500 and the cost of 120 units is 3000.find
the formula connecting c and u,
u when c=4000
c = a + bu
You have
a + 50b = 2500
a + 120b = 3000
Solve for a and b, and then find u when
a + bu = 4000
Or, notice that b increased by 500 when u increased by 70
So, if c increases by another 1000, u will increase by another 140.
Very correct I got it in my lesson thank you very much I will introduce my brothers and sisters to it thank you very much
Yevhemba
Thank you
Well, it sounds like this telephone company has a bit of split personality when it comes to charging! Let's see if we can figure it out.
We know that the cost of 50 units is 2500, and the cost of 120 units is 3000. So, we can start by finding the constant part of the charge.
First, let's calculate the cost per unit:
Cost per unit = (Cost for 120 units - Cost for 50 units) / (120 - 50)
= (3000 - 2500) / 70
= 500 / 70
= 7.14
Now, we can find the constant part of the charge by subtracting the cost of 50 units from the total cost for 50 units and multiplying it by the cost per unit:
Constant part = (Total cost for 50 units) - (Cost per unit * 50)
= 2500 - (7.14 * 50)
= 2500 - 357
= 2143
So, we have the constant part of the charge as 2143. Now let's find the part that varies as the number of units called.
The difference in cost between the constant part and the total cost for a specific number of units will give us the variable part. Using the total cost for 120 units as an example:
Variable part = Total cost for 120 units - Constant part
= 3000 - 2143
= 857
Therefore, the formula connecting the charge (c) and the number of units called (u) would be:
c = 2143 + 7.14u
Now that we have the formula, let's find out the number of units (u) when the charge (c) is 4000.
4000 = 2143 + 7.14u
Subtracting 2143 from both sides:
4000 - 2143 = 7.14u
1857 = 7.14u
Dividing both sides by 7.14:
u = 1857 / 7.14
u ≈ 260
So, when the charge is 4000, the number of units called would be approximately 260.
Hope that brings a little laughter to your telephone charges!
To find the formula connecting the charge (c) and the number of units called (u), we need to determine the constant and the variable components of the charge.
Let's start by finding the constant component of the charge. We are given that the cost of 50 units is $2500. This gives us one equation:
50u = 2500
Now, let's find the variable component of the charge. We are given that the cost of 120 units is $3000. This gives us another equation:
120u = 3000
To find the constant component, we divide the first equation by 50:
u = 50
Now, let's find the variable component by dividing the second equation by 120:
u = 25
So, the constant component is 50, and the variable component is 25.
To get the formula connecting c and u, we can write it as:
c = 50u + 25u
Simplifying this equation, we have:
c = 75u
Now, to find the value of u when c = $4000, we substitute c = 4000 into the formula:
4000 = 75u
To solve for u, divide both sides of the equation by 75:
4000 / 75 = u
Approximately,
u = 53.33
Therefore, when the charge (c) is $4000, the number of units called (u) is approximately 53.33.