Image reduction

To say that I am mathematically challenged is a gross understatement! I'm trying to help my friend determine how to calculate percentages of reduction or enlargement for a quilt pattern.

She is creating a drawing of a cute picture which will become a pieced quilt. When it's done she'll create a pattern with instructions describing how to create the same quilt which customers will purchase. The pattern will be submitted to quilting magazines for selection and publication.

And this is where we get stuck. The finished quilt may measure 36" across (width) by 48" long. BUT. .. The pattern has to be copied onto a magazine page. That page may measure 8.5" x 11".

I cannot seem to find a way to calculate how to reduce the finished quilt size (36 x 48) to fit on the magazine's page requirements--worse, I can't figure out what to type into the instructions to tell the purchaser by what percentage they should enlarge the magazine's printed pattern of my design to end up with the actual finished quilt size.

Can you help me please?

Correct result:

p =  77.0833 %

Solution:

$$\begin{gathered} k_1=8.5\mathrm{/}36={\displaystyle \frac{17}{72}}\doteq 0.2361 \\ {k}_2=11\mathrm{/}48={\displaystyle \frac{11}{48}}\doteq 0.2292 \\ k=min(k_1,k_2)=min(0.2361,0.2292)={\displaystyle \frac{11}{48}}\doteq 0.2292 \\ x=36\cdot k=36\cdot 0.2292={\displaystyle \frac{33}{4}}=8.25\text{ inch } \\ y=48\cdot k=48\cdot 0.2292=11\text{ inch } \\ p=100\cdot (1-k)=100\cdot (1-0.2292)={\displaystyle \frac{925}{12}}=77.0833\mathrm{\%} \end{gathered}$$

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Showing 1 comment:

Dr Math

Reduce dimensions of picture by p = 77.083 % if you want to preserve aspect ratio of your image on magazine page....  But even in this case image will have dimensions 8,25" x 11"  (white bars on sides)

3 years ago  Like

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