The average age of a class of 21 boys is 14year 3month.if the oldest boy is not counted in.the average drops to 14years 2month,how old is he???
Restating what Steve said in a slightly different way:
sum of ages of all 21 boys = 21(14 3/12) = 299 1/4
sum of ages without oldest = 20(14 2/12) = 283 1/3
age of boy not included (oldest)
= 299 1/4 - 283 1/3
= 15 11/12
which is exactly what Steve did
If the oldest boy's age is x, then
(14 3/12)*21 = (14 2/12)*20+x
x = 15 11/12
I don't understand
To find the age of the oldest boy, we need to compare the two averages and calculate the difference.
Step 1: Calculate the total age of the class without the oldest boy:
Average age without oldest boy = 14 years 2 months
Since the average age is given as 14 years 2 months, we can consider it as the sum of the ages of the 21 boys without the oldest boy.
Sum of ages without oldest boy = Average age * Number of boys
= 14 years 2 months * 21
To calculate the sum, we convert the months into a fraction of a year. Assuming 1 year consists of 12 months:
14 years 2 months = 14 + 2/12 years = 14.1667 years
Sum of ages without oldest boy = 14.1667 years * 21 = 297.5 years
Step 2: Calculate the total age of the class with the oldest boy:
Average age with oldest boy = 14 years 3 months
Using the same method as before, we convert the average age into a decimal number of years:
14 years 3 months = 14 + 3/12 years = 14.25 years
Sum of ages with oldest boy = 14.25 years * 21 = 299.25 years
Step 3: Find the age of the oldest boy:
Difference in age = Sum of ages with oldest boy - Sum of ages without oldest boy
= 299.25 years - 297.5 years
= 1.75 years
Since the oldest boy's age is the difference between the two sums, we find that the oldest boy is 1.75 years older than the average age without him.
To calculate the age in years and months, we can convert the decimal part into months. Assuming 1 year consists of 12 months:
Age in months = 1.75 years * 12 = 21 months
Therefore, the oldest boy is 1 year and 21 months older than the average age without him.