   SEARCH HOME Math Central Quandaries & Queries  Question from David, a student: The saddle height on a bicycle should be 109% of the inside leg measurement of the rider (www.harriscyclery.com). If the saddle height is 37 in., then what is the inside leg measurement? I don't know how to set up the equation if you can teach me how to set it up it would be great thanks Hi David,

Percentage questions like this are straightforward to translate into an equation if you read the sentence carefully and compare it to reading an equation. When you read an equation, for example 5x = 6 "five x is equal to 6", you realize that the equal sign is the verb. Thus from your sentence

The saddle height on a bicycle should be 109% of the inside leg measurement of the rider

I see

The saddle height on a bicycle = 109% of the inside leg measurement of the rider

Next, "of" is multiplication ("one half of 12 is 6" is "1/2 × 12 = 6"), and thus your sentence is

The saddle height on a bicycle = 109% × the inside leg measurement of the rider

To make the notation simpler let S be the saddle height of the bicycle and I be the inside leg measurement of the rider. Hence we have

S = 109% × I

Finally 109% is 109/100 = 1.09 so

S = 1.09 × I

Harley     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.