Boys Wearing Glasses

Date: 07/07/99 at 23:36:16
From: justin potillo
Subject: Fractions in word problems

There are 1400 pupils in a school. 1/4 of those wear spectacles and 
2/7 of them are boys. How many boys in the school wear spectacles?

I don't know how to answer this problem. Help!

Date: 07/08/99 at 16:43:35
From: Doctor Rick
Subject: Re: Fractions in word problems

Hi, Justin.

My number-one problem-solving advice is: take it one step at a time.

Can you answer this question: how many pupils in the school wear 
spectacles? The answer is 1/4 of 1400, or

     1/4 * 1400 = ?

Now can you answer the main question: if 2/7 of these students are 
boys, how many spectacle-wearing boys are there?

If you're still confused, maybe a diagram will help. This box contains 
all the pupils in the school:

     +---------------------------+
     |                           |
     |                           |
     |                           |
     |                           |
     |                           |
     |                           |
     |                           |
     |                           |
     |                           |
     +---------------------------+

Of these pupils, 1/4 wear spectacles -- those in the shaded box:

     +-------------+-------------+
     |/////////////|             |
     |/////////////|             |
     |/////////////|             |
     |/////////////|             |
     +-------------+-------------+
     |             |             |
     |             |             |
     |             |             |
     |             |             |
     +---------------------------+

Of those in the shaded portion, 2/7 are boys:

     +-+-+-+-+-+-+-+-------------+
     |XXX|/////////|             |
     |XXX|/////////|             |
     |XXX|/////////|             |
     |XXX|/////////|             |
     +-+-+-+-+-+-+-+-------------+
     |             |             |
     |             |             |
     |             |             |
     |             |             |
     +---------------------------+

Those in the "/" region are not boys, and those in the unmarked region 
don't wear spectacles, so only those in the "X" region are boys who 
wear spectacles. If you can figure what fraction of the total this is, 
then you can find the answer to the question in one more step.

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