Question 120402
Let b=# of boys, g=# of girls



Since "there are 10 more boys than girls in a class", this means we have the first equation: {{{b=10+g}}}. Also if we have the statement "If one more girl joins the class, there will be twice as many boys as there are girls", then we have the second equation: {{{b=2(g+1)}}}





Start with the given system

{{{b=10+g}}}
{{{b=2(g+1)}}}




{{{2(g+1)=10+g}}}  Plug in {{{b=2(g+1)}}} into the first equation. In other words, replace each {{{b}}} with {{{2(g+1)}}}. Notice we've eliminated the {{{b}}} variables. So we now have a simple equation with one unknown.



{{{2g+2=10+g}}} Distribute




{{{2g=10+g-2}}} Subtract 2 from both sides



{{{2g-g=10-2}}} Subtract g from both sides



{{{g=10-2}}} Combine like terms on the left side



{{{g=8}}} Combine like terms on the right side



So there are 8 girls in the class





Now that we know that {{{g=8}}}, we can plug this into {{{b=2(g+1)}}} to find {{{b}}}




{{{b=2((8)+1)}}} Substitute {{{8}}} for each {{{g}}}



{{{b=18}}} Simplify



So there are 18 boys in the class



So our answer is {{{g=8}}} and {{{b=18}}} which means there are 8 girls and 18 boys in the class.