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.

Answer 1

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.