Measuring Material

Date: 07/04/2003 at 23:51:24
From: Maggie
Subject: Inches to yards

I need 225 4-inch squares cut from cotton material.  If the material 
is 30 inches wide, how many yards of material will I need?

Date: 07/05/2003 at 14:54:15
From: Doctor Rick
Subject: Re: Inches to yards

Hi, Maggie.

There are several ways you could approach this. 

The first is by area. Each square you need has an area of 4 inches * 
4 inches = 16 square inches. The area of 225 such squares is 225 * 16 
= 3600 square inches. Now, we want to find a rectangle that is 30 
inches long whose area is 3600 square inches. The area is the length 
times the width:

  ____ * 30 inches = 3600 square inches

What number goes in the blank? It's 3600 divided by 30 = 120 inches.

How many yards is this? There are 36 inches in each yard, so the 
question is, into how many 36-inch pieces can you divide 120 inches? 
That is, 120 divided by 36 = 3 1/3 yards. That's how many yards you 
need. If you can only buy a whole number of yards, you must buy 4 
yards.

Another approach is to actually figure out how you would cut the 
material. This can be more accurate, in cases where you can't cut the 
fabric into the required pieces without some waste.

How many 4-inch squares can we lay out side by side across the width 
of the fabric? The fabric is 30 inches across; into how many 4-inch 
pieces can 36 inches be divided? That's 30 / 4 = 7 1/2 pieces. We've 
got a problem: a 1/2 square won't do, we must have whole squares. Thus 
all we can really get in a row is 7 squares.

How many rows will you need? To answer this, you need to divide 225 
squares into groups of 7. That's 225 / 7 = 32 1/7 rows. Again we don't 
have a whole number, but we don't do the same thing to resolve it. We 
get 7 * 32 = 224 squares in 32 rows; then we need a 33rd row for the 
last square. We need to round UP from 32 1/7 to 33 rows.

How much length do the 33 rows occupy? Each is 4 inches along the 
length of the cloth, so the total length is 4 inches times 33 = 132 
inches. In yards, that's 132 / 36 = 3 2/3 yards; if you can only buy 
whole yards, you must again round up to 4 yards.

The answer came out the same in the end if you must buy a whole 
number of yards, but you see that the second method told us we needed 
1/3 yard more than the first method. That's because, when we actually 
lay out the squares, we find that we have to throw out a strip 2 
inches wide. The first method couldn't take account of this waste. 
That's why the second method is more accurate.

Does this help?

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

Date: 07/06/2003 at 02:15:19
From: Maggie
Subject: Thank you (inches to yards)

Dear Dr. Rick,

I understand now.  I reworked the problem a couple of times and had no 
problem coming up with the same answer. Thank you for your fast help.

- Maggie