SOLUTION: A robot can produce a total of 80 cars in 5 days. Each day it produces 4 less cars than the day before. How many cars does the robot produce a day?

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Question 964257: A robot can produce a total of 80 cars in 5 days. Each day it produces 4 less cars than the day before. How many cars does the robot produce a day?



Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
A robot can produce a total of 80 cars in 5 days. Each day it produces 4 less cars
than the day before. How many cars does the robot produce a day?
This is an arithmetic sequence of n = 5 terms where the common difference is
d = -4.  d is negative because the terms get smaller by 4 each day.  The sum
S5 = 80.

We use the formula, substitute the give numbers and solve for first term a1.

S%5Bn%5D=expr%28n%2F2%29%282%5E%22%22a%5B1%5D%2B%28n-1%29d%29

S%5B5%5D=expr%285%2F2%29%282%5E%22%22a%5B1%5D%2B%285-1%29%28-4%29%29

80=expr%285%2F2%29%282%5E%22%22a%5B1%5D%2B%284%29%28-4%29%29

80=expr%285%2F2%29%282a%5B1%5D-16%29

Multiply both sides by 2

160=%285%29%282a%5B1%5D-16%29%29

160=10a%5B1%5D-80%29%29

240=10a%5B1%5D

24=a%5B1%5D

So the first term is 24.

The question is:

How many cars does the robot produce a day?
That's an odd question, for the answer depends on which 
day is being asked about:

On the 1st day the robot produces 24 cars.
On the 2nd day the robot produces 20 cars.
On the 3rd day the robot produces 16 cars.
On the 4th day the robot produces 12 cars.
On the 5th day the robot produces  8 cars.
------------------------------------------
                    Grand total = 80 cars.


So that's an AVERAGE of 80/5 = 16 per day.  Maybe that's what
the question was supposed to have been.

Edwin