Counting StudentsDate: 10/06/98 at 12:57:13 From: kerry Subject: Say What?! The principal asked Mr. Black how many students there were in his non- graded math class. "Well," Mr. Black replied, "3/4 of them are less than 16 years old, 2/3 are less than 15 years old, 12 are not yet 14 years old, and there are twice as many between the ages of 14 and 15 as there are between the ages of 15 and 16." The principal murmered his thanks and went off to determine how many students there were altogether. After some thought he was able to figure out the correct mumber. Re-construct his logic. Date: 10/06/98 at 17:28:03 From: Doctor Rick Subject: Re: Say What?! Hi, Kerry. I have to tell you that I first solved this one using some algebra, but you probably haven't started algebra yet, so I'll show you another way. Let's make a diagram. Divide the class into four groups: under 14, 14 to 15, 15 to 16, and over 16: +---------+---------+---------+---------+ | | | | | | 12 | | | | | | | | | +---------+---------+---------+---------+ 14 15 16 <====== 2/3 ======> <============ 3/4 ==========> I put down most of the information you have: 2/3 of the students are in the first two boxes, 3/4 are in the first 3 boxes, and 12 students are in the left box. The other piece of information is that box 2 has twice as many as box 3. If you answer these questions, they should lead you out of the maze you're lost in. 1. What fraction of the students are in box 4? (Think: what's left?) 2. What fraction are in box 3? (Subtract fractions.) 3. Can you use the last piece of information to find the fraction in box 2? 4. Now what is the fraction in box 1? 5. Can you see your way out now? - Doctor Rick, The Math Forum http://mathforum.org/dr.math/ |
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