SOLUTION: There are 10 more boys than girls in a class. If one more girl joins the class, there will be twice as many boys as there are girls. How many boys and how many girls are there in

Algebra ->  Customizable Word Problem Solvers  -> Numbers -> SOLUTION: There are 10 more boys than girls in a class. If one more girl joins the class, there will be twice as many boys as there are girls. How many boys and how many girls are there in      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 120402: There are 10 more boys than girls in a class. If one more girl joins the class, there will be twice as many boys as there are girls. How many boys and how many girls are there in the class?
Found 2 solutions by jim_thompson5910, stanbon:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%2Bg. 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%28g%2B1%29




Start with the given system
b=10%2Bg
b=2%28g%2B1%29



2%28g%2B1%29=10%2Bg Plug in b=2%28g%2B1%29 into the first equation. In other words, replace each b with 2%28g%2B1%29. Notice we've eliminated the b variables. So we now have a simple equation with one unknown.


2g%2B2=10%2Bg Distribute



2g=10%2Bg-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%28g%2B1%29 to find b



b=2%28%288%29%2B1%29 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.





Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
There are 10 more boys than girls in a class. If one more girl joins the class, there will be twice as many boys as there are girls. How many boys and how many girls are there in the class?
-----------------
Original numbers:
Let number of girls be "x", then number of boys is "x+10".
-----------------------
Numbers after the change:
# of girls = x+1 ; # of boys is still "x+10"
--------------------------------
EQUATION:
x+10 = 2(x+1)
x+10 = 2x+2
x = 8 (original # of girls) ; x+10 = 18 (original # of boys)
--------------------------------
Cheers,
San H.