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 3 hours to make the dress, it costs #2700. If it takes 5 hours to make the dress, it costs# 3100. Find the cost if it takes 1(1÷ 2) hours to make the dress.
Let's say the constant cost of making the dress is C and the variable cost per hour is V.
From the given information, we have the following two equations:
3V + C = 2700 -- Equation (1)
5V + C = 3100 -- Equation (2)
To find the cost if it takes 1(1/2) hours to make the dress, we need to substitute the appropriate value of V into either of the equations.
First, let's eliminate C from the equations by subtracting Equation (1) from Equation (2):
(5V + C) - (3V + C) = 3100 - 2700
2V = 400
V = 400/2
V = 200
Now we know that the variable cost per hour is 200. We can substitute this into Equation (1) to find the constant cost:
3(200) + C = 2700
600 + C = 2700
C = 2700 - 600
C = 2100
Therefore, the constant cost of making the dress is #2100.
Now let's substitute the values of C and V into the equation to find the cost if it takes 1(1/2) hours to make the dress:
1(1/2)(200) + 2100
300 + 2100 = 2400
Therefore, if it takes 1(1/2) hours to make the dress, it will cost #2400.
To find the cost if it takes 1(1/2) hours to make the dress, let's first determine the variable cost per hour.
Let's assume the constant cost of making the dress is C and the variable cost per hour is V.
From the given information, we have two data points:
- When the dress takes 3 hours to make, it costs #2700: Cost = C + 3V = #2700
- When the dress takes 5 hours to make, it costs #3100: Cost = C + 5V = #3100
We can now solve this system of equations to find the values of C and V.
From equation 1: C + 3V = #2700
From equation 2: C + 5V = #3100
Let's solve this system using the elimination method.
Multiply equation 1 by 5 and equation 2 by 3 to eliminate C.
5(C + 3V) = 5(#2700)
3(C + 5V) = 3(#3100)
5C + 15V = #13500
3C + 15V = #9300
Now subtract the second equation from the first equation:
(5C + 15V) - (3C + 15V) = #13500 - #9300
2C + 0 = #4200
2C = #4200
Divide both sides by 2:
C = #2100
Now substitute the value of C back into any of the original equations to find the value of V:
C + 3V = #2700
#2100 + 3V = #2700
3V = #2700 - #2100
3V = #600
Divide both sides by 3:
V = #600 / 3
V = #200
Now we have the values for C and V. The cost equation is:
Cost = C + Time (in hours) * V
Cost = #2100 + 1.5 * #200 (since 1(1/2) hours is equal to 1.5 hours)
Cost = #2100 + #300
Cost = #2400
Therefore, if it takes 1(1/2) hours (1.5 hours) to make the dress, the cost would be #2400.