SOLUTION: The average age of 30 boys in a class is 15 years. One boy aged 20 years, left the class, but two new boys came in his place whose age differ by 5 years. If the average age of all

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Question 935712: The average age of 30 boys in a class is 15 years. One boy aged 20 years, left the class, but two new boys came in his place whose age differ by 5 years. If the average age of all the boys now in the class remains 15 years, the age of the youngest new comer is?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
the average age of the boys is 15.
the number of boys is equal to 30
the total age of the boys is equal to 15*30 = 450
one boy aged 20 leaves the group.
2 other boys join the group.
the boys differ in age by 5 years.
let x equal the age of one of the boys.
let x + 5 equal the age of the other of the boys.
there were 30 boys to start with.
now there are 31 (30 - 1 + 2 = 31).
the average age of the boys is still 15.
you get:
(450 - 20 + x + x + 5) / 31 = 15
simplify by combining like terms to get:
(450 - 15 + 2x) / 31 = 15
multiply both sides of this equation by 31, and simplify further by combining the constants together, to get:
435 + 2x = 465
subtract 435 from both sides of the equation to get:
2x = 30
divide both sides of the equation by 2 to get:
x = 15
the boys that are added are aged 15 and 20.
the age of the youngest is 15.
that's your solution.