How Many Boys Are in the Seventh Grade?

Date: 05/20/99 at 15:52:20
From: Akj
Subject: Word problem

I can't do this word problem. My answer always comes out in decimal 
form and it's not supposed to:

In a seventh grade of 360 students, 80 percent of all students can 
swim. 90 percent of the girls can swim, and 180 of the boys can swim. 
How many boys are in the seventh grade?

Date: 05/22/99 at 14:48:49
From: Doctor Jeremiah
Subject: Re: Word problem

Hi there.

The hard part of word problems is figuring out what equations the 
words mean.

Let "b" be the total number of boys.
Let "g" be the total number of girls.

The boys and girls together make 360:

b + g = 360

The total that can swim is the girls that can swim + the boys that can 
swim:

 80% of 360 = 90% of g + 180

So now we have two equations and two unknowns (b and g):

      b + g = 360
   0.80*360 = 0.90*g + 180

Solve the second one:

   0.80*360 = 0.90*g + 180
        288 = 0.90*g + 180
  288 - 180 = 0.90*g + 180 - 180
        108 = 0.90*g
        108 = g*0.90
   108/0.90 = g*0.90/0.90
        120 = g*1
        120 = g

Now that we now "g" we can solve the first one:

        b + g = 360
        b + g = 360  <==  120 = g
      b + 120 = 360
b + 120 - 120 = 360 - 120
            b = 240

So there are 240 boys.

Since you never got the right answer, do you know what went wrong?

- Doctor Jeremiah, The Math Forum
  http://mathforum.org/dr.math/