Question 935712
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.