Associated Topics || Dr. Math Home || Search Dr. Math

### Pencil Costs, Dividing Property

```
Date: 6/25/96 at 4:50:14
From: Susan Goh
Subject: Pencil Costs and Dividing Property

Dear Dr. Math,

Drawing pencils cost 8 cents each and colored pencils cost 11 cents
each. Two dozen assorted pencils cost \$2.16. How many colored pencils
are there?

Another one, but this is more of a puzzle:

A man died, leaving behind 23 cows to his three children. His will
states that the eldest child should have 1/2 of the fortune, the
second child 1/3 and the youngest 1/8 of the total fortune. How can
the three children divide the animals among themselves so that it is
not necessary to kill any animal?

A wise man came to the scene. He brought along his only cow and put it
with the other 23 cows to give a total of 24 cows. He gave 1/2 of the
24 cows to the eldest child, i.e. 12 cows; 1/3 of the 24 cows to the
second child, and 1/8 of the 24 cows to the youngest. He went away
with his only cow. Can you discover the clue to this solution?

SOS.   Jean
```

```
Date: 6/25/96 at 12:3:7
From: Doctor Lisa
Subject: Re: Pencil Costs and Dividing Property

In this problem, let x = the number of colored pencils and 24-x = the
number of drawing pencils.  This is possible because the colored
pencils and the drawing pencils have to add up to 24.  If you knew you
had 10 colored pencils, then to get the number of drawing pencils,
you'd take 24-10 = 14.  So the equation set up would be (using cents):

8(24-x) + 11(x) = 216.

The remainder of the work goes as follows:

192 - 8x + 11x = 216 (distributing the 8 in the first parentheses)
192 + 3x = 216       (combining like terms)
3x = 24              (subtracting 192 from both sides)
x = 8                (dividing both sides by 3)

So you would have 8 colored pencils (and 16 drawing pencils).

In the second problem, the part with the wise man coming to the scene
makes the problem clearer.  If you use 24, it is very easy to come up
with 1/2, 1/3, and 1/8 of that number since 2, 3, and 8 all go into 24
evenly. This means that the eldest would get 12 cows, the second would
get 8 cows, and the youngest would get 3 cows.  If you add up 12, 8,
and 3, you get 23 (and thus the wise man can take his cow with him).

Hope this helps!

-Doctor Lisa,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```

```
Date: 6/25/96 at 12:27:40
From: Doctor Anthony
Subject: Re: Pencil Costs and Dividing Property

Yes, if you add 1/2 , 1/3 and 1/8 you get 23/24.  So the old man is
dividing his estate in the RATIO 1/2 : 1/3 : 1/8, which is 12 : 8 : 3
and by good fortune that adds up to 23.  1/24th part of his estate was
not allocated to anyone, so if he had had 24 cows, there would have
been one cow left over.

-Doctor Anthony,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
Middle School Word Problems

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search