The cost of making a dress is partly constant and partly varies with the amount of time it takes to make the dress.if the dress takes 3hrs to make,it cost #2700.if it takes 5hrs to make dress,it cost #3100.find the cost if it takes 1½hours to make the dress.
cost = a + bt, where a and b are constants and t is the time to make a dress in hours.
from your given:
a + 3b = 2700
a + 5b = 3100
subtract them
2b = 400
b = 200
now that you have b, find a from one of the equations.
given you the complete equation.
sub in t = 1.5 to get the cost
Well, well, well, let's calculate it with a twist!
First, we need to find the constant cost, which is the same regardless of the time taken. To do that, we can subtract the variable cost from the total cost when it takes 3 hours to make the dress:
Total cost when it takes 3 hours = #2700
Variable cost when it takes 3 hours = Total cost when it takes 3 hours - Constant cost
Variable cost when it takes 3 hours = #2700 - Variable cost
Now, let's find the variable cost per hour:
Variable cost per hour = Variable cost when it takes 3 hours / 3 hours
Once we've got the variable cost per hour, we can find the total cost for any given time. Here's how we do it:
Total cost = Constant cost + (Variable cost per hour × Time taken)
Now it's time to put this theory into practice and put a smile on your face. Ready? Let's go!
Variable cost when it takes 3 hours = #2700 - #x
Variable cost per hour = (Variable cost when it takes 3 hours) / 3
Total cost = #x + (Variable cost per hour × Time taken)
Now, for the grand finale! When it takes 1½ hours to make the dress, we plug in the values and voila:
Total cost = #x + (Variable cost per hour × 1½)
Here, 1½ hours = 1.5 hours (to avoid confusion with the mathematical symbol for square root)
So, the witty answer to your question is...
drumroll, please...
The cost, my dear friend, if it takes 1½ hours to make the dress, is #x + (Variable cost per hour × 1.5).
Now that wasn't too bad, was it?
To solve this problem, we can set up a linear equation. Let's assign the constant cost as "a" and the cost per hour as "b".
From the given information, we have two equations:
1) 3a + 3b = 2700 (when the dress takes 3 hours to make)
2) 5a + 5b = 3100 (when the dress takes 5 hours to make)
To find the cost if it takes 1 ½ hours to make the dress, we need to substitute 1.5 for the time in the equation and solve for the cost.
So, let's solve the two equations above to find the values of a and b:
From equation 1:
3a + 3b = 2700
Simplifying, we get:
a + b = 900 -- (equation 3)
From equation 2:
5a + 5b = 3100
Simplifying, we get:
a + b = 620 -- (equation 4)
Now, we have a system of equations (equations 3 and 4) to solve:
a + b = 900 -- (equation 3)
a + b = 620 -- (equation 4)
By subtracting equation 4 from equation 3, we can eliminate b:
(a + b) - (a + b) = 900 - 620
0 = 280
The result is 0 = 280, which is not possible. This means that the system of equations is inconsistent, and there is no unique solution for a and b.
Therefore, we cannot determine the exact cost of making the dress if it takes 1½ hours.
To solve this problem, we need to determine the constant cost and the variable cost per hour.
Let's say the constant cost is represented by C, and the variable cost per hour is represented by V.
We are given two data points:
1. When the dress takes 3 hours to make, it costs #2700.
So, we have the equation: C + 3V = 2700. (Equation 1)
2. When the dress takes 5 hours to make, it costs #3100.
So, we have the equation: C + 5V = 3100. (Equation 2)
We can solve these two equations simultaneously to find the values of C and V.
To do this, subtract Equation 1 from Equation 2:
(C + 5V) - (C + 3V) = 3100 - 2700
Simplifying, we get:
2V = 400
Divide both sides of the equation by 2:
V = 200
Now, substitute the value of V back into either Equation 1 or Equation 2. Let's use Equation 1:
C + 3(200) = 2700
Simplifying, we get:
C + 600 = 2700
Subtract 600 from both sides of the equation:
C = 2700 - 600
C = 2100
Therefore, we have the constant cost (C) = #2100 and the variable cost per hour (V) = #200.
Now, to find the cost if it takes 1½ hours to make the dress:
Substitute the value of time (1½ hours = 1.5 hours) into the equation: C + (1.5 * V)
Cost = 2100 + (1.5 * 200)
Cost = 2100 + 300
Cost = #2400
So, if it takes 1½ hours (1.5 hours) to make the dress, the cost will be #2400.