Math question

[John Connor]

Okay, I'm about average when it comes to math and I can kinda figure things out for my self, but I'm a little stumped on this question. My mom makes doll clothes and sells them on Ebay she wants to take a 6" pattern and increase its size to fit a 10" doll. I was thinking that would be a factor of 40% but that would be too large. She figures it's around 25%. How do I solve this? Please explain your steps so I can learn how to do this, thanks!

 

[Binky]

10 / 6 - 1 = 67% larger

Percentage change is generally measured in relation to the starting point. Something that is 10" is 67% larger than something that is 6", since the 4" change is 67% of the base (6").

I'm not sure if this would translate to a doll, since this would assume that everything increases in the same proportions, which is probably not true at all. A 10" doll probably wouldn't be much wider than the 10" doll. Certainly not 67% wider.

 

[Paul98]

Okay, I'm about average when it comes to math and I can kinda figure things out for my self, but I'm a little stumped on this question. My mom makes doll clothes and sells them on Ebay she wants to take a 6" pattern and increase its size to fit a 10" doll. I was thinking that would be a factor of 40% but that would be too large. She figures it's around 25%. How do I solve this? Please explain your steps so I can learn how to do this, thanks!

yes the 10" is 67% more than the 6". But that is assuming all dimensions increase the same amount. But that isn't going to happen. If you have a 6" to compare to a 10" you can check the dimensions and see how much they actually increase. Then take that percentage increase to figure out the new size.

 

[drinkmorejava]

Are you trying to figure out how much more material you will need? If we're talking areas, that's going to increase more with the square of height. Thus:

Old area required 6x6=36in^2
New area required 10x10=100in^2
=178%

You'll need the actual shape to really figure it out though. I just assumed a square.

 

[John Connor]

67% sounds too big. My mom was saying that if you increased a 6" pattern by 50% it would fit a 12" doll.

 

[DrPizza]

67% sounds too big. My mom was saying that if you increased a 6" pattern by 50% it would fit a 12" doll.

Maybe your mom isn't good at math either? A 6" pattern is 50% the size of a 12 inch. Assuming the doll remains proportional, and I don't see why one wouldn't - then all of the lengths scale of proportionally at 67% larger. (It's ten sixths the size, so an increase of four sixths, by length.) As drinkmorejava pointed out, the *area* scales up with the square of the length. So, it'll use 10/6 squared more, or 100/36 or 2.78 times as much fabric. His 178% is a typo (should be 278%).

 

[Xtrem]

Please explain what this "doll" is or looks like

 

[sao123]

67% sounds too big. My mom was saying that if you increased a 6" pattern by 50% it would fit a 12" doll.

6" - > 12" = 100% increase.
6" + (100%) * 6" = 12"
6" + 1 * 6" = 12"
6" + 6" = 12"


if it was 50%...

6" + (50% * 6") = ?
6" + (1/2 * 6") = ?
6" + 3" = 9"
9"

 

[Mr. Pedantic]

Okay, I'm about average when it comes to math and I can kinda figure things out for my self, but I'm a little stumped on this question. My mom makes doll clothes and sells them on Ebay she wants to take a 6" pattern and increase its size to fit a 10" doll. I was thinking that would be a factor of 40% but that would be too large. She figures it's around 25%. How do I solve this? Please explain your steps so I can learn how to do this, thanks!

I'm not quite sure what kind of math I'm seeing here...

Does she mean that 6 is 50% of 12? Cause if that's the case then 6 is 60% of 10. Or does she mean that 6 is 12 minus 50% of 12? If that's the case, then 10 - 0.4x10 = 6.

If you want the conventional method of calculating percentages and fractions, then 6 x 1.666... = 10.

Either way, you probably aren't average at math...

 

[John Connor]

All I know is that when she wanted a pattern reduced from a 17" doll to 5" I simply dived 5 by 17 to get a percent and that worked. Now all I need to do is increase from a 6" pattern to fit a 10" doll. The percentage is used on the copy machine.

 

[John Connor]

Please explain what this "doll" is or looks like

Go to Ebay and type in OOAK baby dolls. My mom is in a forum with many artist that sell on Ebay and real life-like baby dolls made from plastic. Richard Simmons collects them.

 

[Binky]

5 / 17 = 29%, so it's 29% of the original size (71% reduction)
10 / 6 = 167%, so it's 167% of the original size (67% increase)

The math is the same.

 

[John Connor]

10 / 6 = 167%, so it's 167% of the original size (67% increase)

The math is the same.

This what I was thinking, but my mom says if you increased a doll pattern that was 6" by 50% that would fit a 12" doll so 67% sounds too big.

 

[Mr. Pedantic]

This what I was thinking, but my mom says if you increased a doll pattern that was 6" by 50% that would fit a 12" doll so 67% sounds too big.

She's wrong.

There is actually no way which you could charitably interpret what she said and arrive at the conclusion that what she said makes sense. Increasing 6 by 50% does not result in 12, it results in 9.

 

[intx13]

Depending on the context, there are two different ways to think about scaling with percentages.

The first method is the multiplicative method. This is the method used by the "scale" command in most computer graphics programs, like Photoshop. You provide a percentage and the new image is that percentage multiplied by the original image.

For example, if you entered "50%" the new image would be 50% times the original image; that is, half the size of the original image. If you entered "200%" the new image would be 200% times the original image; that is, twice the size of the original image. If you entered "100%" the new image would be exactly the same size as the original image.

The second method is the additive method. This is the method many people use when talking out loud, but personally I think it's a little confusing. In this method you specify the percentage by which to increase the original image. You cannot shrink the image.

For example, if you said "50%" the new image would be 50% bigger than the original image. If you said "100%" the new image would be 100% bigger than the original image; that is, twice the size. If you said "0%" the new image would be 0% bigger than the original image; that is, the new image would be exactly the same size as the original image.

It's easy to convert from multiplicative scaling to additive scaling. To go from multiplicative to additive, subtract 100%. To go from additive to multiplicative, add 100%.

Now let's take your mom's problem. You've got a pattern for a 6" doll and you want to create a pattern for a 10" doll. To get the multiplicative scaling factor, just divide the new size by the old size and multiply by 100. 10"/6" * 100 = 167%. This means that if you were scaling the image in Photoshop you would enter "167%" as the multiplicative scaling factor.

To get the additive scaling factor, subtract 100% from the multiplicative scaling factor. 167% - 100% = 67%. This means that if someone asks you how much bigger should the new pattern be, you would answer "67% bigger".

Now let's figure out why your mom's answer ("50% bigger") was wrong. She said "bigger" so she clearly meant "additive scaling". First, let's convert it to a multiplicative scaling factor by adding 100%. 50% + 100% = 150%. So if she were scaling the pattern in Photoshop she would have entered "150%". Now let's figure out how big her new doll would be. 6" * 150 / 100 = 9". That's too small, so her guess of "50% bigger" was too low.

In conclusion, if your mom is using Photoshop to scale up her pattern, she should enter "167%" as the scale factor. If she's telling someone how much bigger the new pattern should be, she should tell them "67% bigger". If she's drawing a new pattern on paper, she should move her pencil 1.67 inches for each inch of the original pattern.

 

[John Connor]

She is using a copy machine to increase or decrease the size of the pattern.