SOLUTION: A group of workers was supposed to make 768 vacuum cleaners in a certain amount of time. For the first five days, the team made exactly the number of vacuum cleaners they were supp

Question 1075487: A group of workers was supposed to make 768 vacuum cleaners in a certain amount of time. For the first five days, the team made exactly the number of vacuum cleaners they were supposed to make in order to be finished by their deadline. For the rest of the time they made 6 more vacuum cleaners each day than they were supposed to and so the day before the deadline they already had 844 vacuum cleaners. How many vacuum cleaners was the group supposed to make each day? Show your work!
Answer by ikleyn(52855) (Show Source): You can put this solution on YOUR website!
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A group of workers was supposed to make 768 vacuum cleaners in a certain amount of time. For the first five days,
the team made exactly the number of vacuum cleaners they were supposed to make in order to be finished by their deadline.
For the rest of the time they made 6 more vacuum cleaners each day than they were supposed to and so the day before the deadline
they already had 844 vacuum cleaners. How many vacuum cleaners was the group supposed to make each day? Show your work!
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let "n" be the originally scheduled number of days and "r" be the rate of work of the entire team, 

    measured in .

Then 

nr = 768   (1)

is your first equation.

The second equation is 

5r + (n-6)*(r+6) = 844.   (2)

I leave it on your own to get understanding why it is so. (It is ELEMENTARY).


Simplify (2):

5r + nr - 6r + 6n - 36 = 844,

5r + 768 - 6r + 6n - 36 = 844,       (I replaced here nr by 768 due to (1))

-r + 6n = 844 - 768 + 36,

-r + 6n = 112

From the last equation express r = 6n - 112 and substitute it into (1). You will get

(6n-112)*n = 768 --->   = 0,  --->

 =  = .

The only positive root is n =  = 24.

Answer.  The originally scheduled number of days was 24.

         The originally planned rate of work was  = 32 vacuum cleaner per day.

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