Three Pieces of Wire

Date: 01/07/98 at 22:11:58
From: Email
Subject: I need serious help

Here is my math problem. I have no idea how to figure it out:

A florist cuts a wire into 3 pieces. The 1st piece is 20% of the 2nd. 
The 3rd piece is 110% of the 2nd. The wire is 23 cm long. What is the 
length of each piece?

Erin

Date: 01/08/98 at 13:02:39
From: Doctor Joe
Subject: Re: I need serious help

Hi Erin,

This problem requires some simple algebra: 

First, let x denote the length of the 2nd piece of wire (in cm).

It follows that the length of the first piece, which is 20% of the 
first, can be expressed as (20%)*(x), where * denotes the usual 
multiplication. So, we have: 0.2x because 20% is actually 20/100 = 0.2

Similarly, the length of the third piece can be found:
(110%)*(x) = 1.1x

Finally, we add the lengths of the three pieces:

First wire + Second Wire + Third Wire = Total Length

So,

0.2x + x + 1.1x = 23

Then, adding the terms on the left, we have 2.3x = 23.

Finally, multiplying by 1/(2.3), which is the reciprocal of 2.3,

we have:  x = 23/(2.3) = 10.

Thus, the 2nd piece of wire measures 10 cm. The first wire is 20% of 
10cm = 2cm, and the third measures 110% of 10cm = 11cm.

As a last step, check that the three pieces sum to a total of 23 cm:

2 + 10 + 11 = 23.

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