The cost of making a dress is partly constant and partly varies with the amount of time it takes to make the dress, if a dress take 3 hours to make it cost #2700 if it takes 5 hours to make it cost#3100 find the cost if it takes 1/2 hours to make the dress
Let the constant cost of making the dress be C and the cost per hour of making the dress be P.
Given that it costs #2700 to make the dress in 3 hours, we can set up the equation:
C + 3P = 2700
Given that it costs #3100 to make the dress in 5 hours, we can set up the equation:
C + 5P = 3100
Now we have a system of two equations:
C + 3P = 2700
C + 5P = 3100
Subtracting the first equation from the second equation, we get:
2P = 400
P = 200
Now that we have found the cost per hour of making the dress, we can substitute this back into one of the original equations to find the constant cost C:
C + 3(200) = 2700
C + 600 = 2700
C = 2100
So, the cost of making the dress in 1/2 hours would be:
C + (1/2)200
2100 + 100
= #2200
Therefore, the cost of making the dress in 1/2 hours would be #2200.