Word Problems 7 & 8
Problem 7: There are 40 boys in a class. One of them weighing 100 lbs goes away, a new boy joins the class at the same time. The average weight of the boys is thus increased by 1/4 lbs, Find the weight of the new boy.
Suppose there are 39 boys in class whose weight is x1,x2,x3 ………x39 and one boy (40th) has wieght of 100lb.
So their average weight is ‘y’ then;
Now suppose 100lb boy leaves away and new boy comes whose weight is ‘zlb’
Then again average weight of 40 including new boys is calculated as;
Put values of x1+x2+x3+……..+x39 from eq (1) above, we get;
So, the weight of new boy is 110 lb
Problem 8: The average age of a class of 20 boys is 14.95 years. The avaerage age of the class is raised to 15 years by the arrival of a new student. How old is that new boy?
Let’s suppose ages of 20 students be x1,x2,x3………………..x20
Then average age of 20 students is obtained by taking sum of their ages and dividing the sum by number of student i-e20;
But average of 20 students is given to be 14.96 in statement;
Let new boy’s age is ‘y’ years
Now average age of total 21 boys is given by;
But average age of 21 students is given to be 15 years
Put value of x1+x2+x3+…….+x20 here;
So, the age of new boy is 16 years