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

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) (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: . 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:

Start with the given system

Plug in into the first equation. In other words, replace each with . Notice we've eliminated the variables. So we now have a simple equation with one unknown.

Distribute

Subtract 2 from both sides

Subtract g from both sides

Combine like terms on the left side

Combine like terms on the right side

So there are 8 girls in the class

Now that we know that , we can plug this into to find

Substitute for each

Simplify

So there are 18 boys in the class

So our answer is and which means there are 8 girls and 18 boys in the class.

Answer by stanbon(75887) (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.

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