SOLUTION: On six days in a week two cities had the same daily average temperature. But because of sudden drop in the temperature on the seventh day in one of the cities the average weekly te

Algebra ->  Average -> SOLUTION: On six days in a week two cities had the same daily average temperature. But because of sudden drop in the temperature on the seventh day in one of the cities the average weekly te      Log On


   

Question 475297: On six days in a week two cities had the same daily average temperature. But because of sudden drop in the temperature on the seventh day in one of the cities the average weekly temperature of the two cities different by 0.42C. how much was the difference between the average daily temperature of the two cities on the seventh day?
a. 2.38C
b. 2.34C
c. 2.94C
d. 2.40C
e. none.
Thanks in advance... :)
Answer by ccs2011(207) About Me  (Show Source):
You can put this solution on YOUR website!
Average = Sum/N
For the week N=7 for seven days.
The difference in the sum is x, this is what we are trying to solve for.
For the first six days they have the same avg therefore the sum is the same for those six days. Let this sum be S.
On the 7th day, say city1 has temp T then city2 has temp T-x because it had a sudden drop.
Therefore the 7 day sum for city1 is S+T and city2 is S+(T-x).
Now set up equation looking at difference in averages which equals 0.42.
%28S%2BT%29%2F7+-+%28S%2BT-x%29%2F7+=+0.42
Combine into 1 fraction
%28S%2BT-S-T%2Bx%29%2F7+=+0.42
Add like terms, notice the S and T cancel
x%2F7+=+0.42
Multiply by 7 on both sides
x+=+2.94
Therefore the difference in the 7th day temps was 2.94 degrees.
Think of it as the one day change of 2.94 degrees only caused a change of 1/7 of the impact on the avg. weekly temperature. Just like this one drastic one-day difference would have even less impact on the avg. monthly temperature.
2.94/30 = .1 so the difference in the avg monthly temp would only be 0.1 degrees.