Christopher R. answered • 11/21/14
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Hi Irina, it is stated in the problem the average amount of gas per race in the last 5 races is 15 gallons. Note: the problem is not as difficult as it sounds.
Let x = the amount of gas gas Jim's car used in the last two races.
The equation for this situation would be simply the sum of the total gas Jim's car used in the first 3 races being 51 gallons and the total number of gallons used in the last two races being x equals to 15 times 5. Note: The product of 15 and 5 is the total gallons of gas Jim's car used in the 5 races.
51+x=15*5=75
-51 -51
x=24 gallons of gas Jim's car used in the last 2 races. Your answer is right. Again, the average gallons per each race is actually stated in the problem. However, the average is not always equal to the actual amount of gallons Jim's car used in each race. An example could be his car use 14 gallons in the first race and 16 gallons in the second. This would make the average being 15 gallons per race.
Christopher R.
Irina, I don't know what level you are in math. The problem doesn't give you enough information to calculate the actual number of gallons for each race. However, if you were given the variance in which you could determine the standard deviation. Standard
deviation is the average in which the number deviates from the average for each race.
S = Standard Deviation = √(1/n*∑(xi-xave)^2) where xi is the recorded number of gallons of gas used in the 'ith' race. However, if you are given the variance in which the standard deviation is the square
root of it, you could use statistics to estimate in which the data falls within the average.
The simple answer is you couldn't determine the actual amount of gas used each race. The actual amount of gas used would depend on the average speed in which Jim drove the car during that race, and other factors such as wind resistence, the efficiency
of the car, etc. Statistics and probability math becomes good tools in doing estimates.
Hope this helps.
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11/21/14
Christopher R.
However, you could determine the average gallons used for each race in the first three races being 51/3 = 17 gallons per race; also, determine the average gallons of gas used in the last two races being 24/2 = 12 gallons per race. If you take the average
of the last two numbers in which is (17+12)/2 = 29/2 = 14.5. This is taking the average of the two averages.
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11/21/14
Irina L.
11/21/14