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 that will become a pieced quilt. When done, she'll create a pattern with instructions describing how to create the same quilt that 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 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 answer:

p =  77.0833 %

Step-by-step explanation:

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

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