Question on work done by #x# machines in some days?

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1 Answer
May 27, 2017

Answer:

Option C

Explanation:

Given that the initial estimated count of machines be #x#
Given that the adjusted count of machines is #x+3#
Given that the new count of days to complete the task is 12 days.

Let the amount of work be measured in 'machine days'.

#color(blue)("Initial condition")#

So the amount of work to complete the work is:

#12(x+3)# machine days.

Set #12(x+3)" machine days "=# the amount of work for 1 job

#12(x+3)=1" "..........................Equation(1)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Changed condition")#

Not 3 but only 1 additional machine is used.

The total amount of work still needs to be done to complete the task.

Let the new count of days be #d#

#d(x+1)=1" "...............................Equation(2)#

Using #Equation(1)# substitute for 1 in #Equation(2)#

#d(x+1)=12(x+3)" ".............................Equation(2_a)#

Divide both sides by #(x+1)#

#d=(12(x+3))/(x+1)#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Determine the number of days more than originally estimated")#

#d-10 " "=" "(12(x+3))/(x+1) -10#

Set the value of #1-=(x+1)/(x+1)" "#so #" "10 -=(10(x+1))/(x+1)#

Thus we have:

#d-10 " "=" "(12(x+3))/(x+1) -10#

#" "=" "(12(x+3))/(x+1)-(10(x+1))/(x+1)#

#" "=" "(12x+36-10x-10)/(x+1)#

#" "=" "(2x+26)/(x+1)#

This matches option C