Question

Dose any one know how to figure this problem out?

Answer 1

Do you know how to do proportions?
\[ \frac{hat size}{head circumference}= \frac{hat size}{head circumference} \]

Answer 2

NO

Answer 3

This video talks about proportions
http://www.khanacademy.org/video/proportionality?playlist=ck12.org+Algebra+1+Examples

It is helpful background. As for your particular problem:

The table is telling you that hat size is related to head size (makes sense!)
In theory, if you know your head size you can figure out what hat size you need,
and vice versa.

How? The problem says "use ratio and proportion". This means the following equation is true:

hat size/head size = k (k is a number, the "proportionality constant")

If you know the hat size and the head size, you can find k.
Once you know k, you can use it:

hat size
----------- = k
(22 4/5)

use algebra to solve for hat size (multiply both sides by 22 4/5)
hat size = k * 22 4/5

So let's find k, using the first row of the table.

7 3/8
------- = k
23 1/5

Are you allowed to use a calculator? Then use it:
(7 + 3/8) 7.375
----------- = ---------- = 0.318 (rounded from 0.317887931)
(23 + 1/5) 23.2

Now figure out the entries for the second row:

hat size
----------- = 0.318
22 4/5

change 22 4/5 to decimal: 22+ 4/5 = 22+0.8= 22.8

hat size
----------- = 0.318
22.8
hat size = 0.318*22.8 (multiply both sides by 22.8)
hat size = 7.2504

We need this to the nearest 1/8. How do we do this?
multiply the fraction by 8, and round to the nearest integer (If this does not
make sense, we need to do another lesson):

0.2504*8= 2.0032. which rounds to 2
Final answer:
hat size = 7 2/8 = 7 1/4

Now to find the head circumference in centimeters, we start all over, and find a different k:

7.375
-------- = k
59

and then, using the hat size we just found,

7 1/4
------------- = k
head (cm)

or, changing 1/4 to 0.25
7.25
------------ = k
head

multiply both sides by head:
7.25 = head * k

divide both sides by k:
7.25
------- = head
k

Be sure to round to the nearest centimeter.

Answer 4

I dont understand the last part

Answer 5

Did you find the new k?

Answer 6

No

Answer 7

ok lets get rid of the stupid mixed number and write
\[7\tfrac{1}{8}=\frac{59}{8}\] and
\[23\tfrac{1}{5}=\frac{116}{5}\] and
\[22\tfrac{4}{5}=\frac{114}{5}\] and you want to solve the proportion

Answer 8

\[\frac{x}{\frac{59}{8}}=\frac{\frac{114}{5}}{\frac{116}{5}}=\frac{114}{116}\]

Answer 9

The head circumference is the one i need