SOLUTION: Greg is participating in a 5 -day cross-country biking challenge. He biked for 49, ,57,50 and 51 miles on the first four days. How many miles does he need to bike on the last day s

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Question 1196983: Greg is participating in a 5 -day cross-country biking challenge. He biked for 49, ,57,50 and 51 miles on the first four days. How many miles does he need to bike on the last day so that his average (mean) is 51 miles per day?

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

The governing equation is

    %2849%2B57%2B50%2B51%2Bx%29%2F5 = 51  miles per day   (average).


The solution is in one line

    last day mileage  x = 51*5 - (49 + 57 + 50 + 51) = 48 miles.

Solved.



Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


The solution method from the other tutor uses the basic definition of average to find the answer. That method is of course fine.

If the numbers being averaged are close together, a different solution method, comparing each number to the desired average, is often easier, because the numbers you have to work with are smaller.

For this example....
  49:  -2
  57:  +6
  50:  -1
  51:   0
 ---------
  sum: +3

Over the first four days, he is 3 miles over what he needs to get an average of 51 miles per day; so on the last day he can be 3 miles short of the desired average.

ANSWER: 51-3 = 48 miles