# Ratios

## Comparisons of two numbers, measurements, or quantities.

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The Perfect Blond

Credit: Ricard Aparicio
Source: http://www.flickr.com/photos/vive-recordando/5665292567/
License: CC BY-NC 3.0

Do you know many people with blond hair? Some people are natural blonds. Others dye their hair blond. One leading manufacturer of hair dyes makes 55 different shades of blond!

#### Why It Matters

How does a bottle of “ash blond” differ from a bottle of “strawberry blond” dye? The key lies with proportions. Commercial hair coloring products are made with a dye that is mixed with many other ingredients. The proportion of dye to other ingredients, such as antioxidants and detergents, determines the shade of hair tint produced. Customers can be sure that each box of dye labeled as a certain color is prepared with a set of proportions that will consistently result in the same color.

Credit: Mainstream Media Distribution Inc.
Source: http://www.flickr.com/photos/gomainstream/9973924413/
License: CC BY-NC 3.0

Hair stylists uses something called the “lift/deposit ratio” to determine which color is best for your hair. Imagine that you are a stylist. Your client, who has light brown hair, would like to be a blond. First, you’ll have to choose a number that represents the color of his hair. The smallest numbers are assigned to dark hair, so this client would be a six. The client desires to lighten his hair two shades, to a level eight. In the language of hairstylists, the client wants a “lift” of two levels. Multiply the desired hair shade (8) by the lift (2), and subtract the level of his natural hair (6):

\begin{align*}8 \times 2 = 16 \end{align*}

\begin{align*}16 - 6=10\end{align*}

This means that you should choose a dye of level ten to create the desired hair color for your client.

#### Explore More

Learn more about the chemistry behind dyeing hair with the following link.

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### Image Attributions

1. [1]^ Credit: Ricard Aparicio; Source: http://www.flickr.com/photos/vive-recordando/5665292567/; License: CC BY-NC 3.0
2. [2]^ Credit: Mainstream Media Distribution Inc.; Source: http://www.flickr.com/photos/gomainstream/9973924413/; License: CC BY-NC 3.0

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