Question 825853
{{{15*5=75}}} is the sum of the ages of the first 5 boys.
When the sixth boy joins them, the sum of the ages of the 6 boys is
{{{75+x}}} , and the average of the ages of the 6 boys is
{{{(75+x)/6}}}
15 years and 6 months ={{{15&1/2}}}{{{years=15.5years}}}
So, {{{(75+x)/6=15.5}}} .
 
Solving:
{{{(75+x)/6=15.5}}}
{{{75+x=15.5*6}}}
{{{75+x=93}}}
{{{x=93-75}}}
{{{x=18}}}
 
Think of it a different way to make it a mental math problem.
The sixth boy must be older than 15.
How much older?
His extra age (over 15) must be enough that divyied up over the 6 boys it would add {{{1/2}}} year to the average.
{{{(1/2)*6=3}}}
SO that sixth boy is 3 years older than the average, and {{{15+3=highlight(18)}}} .