Question

A bolt is to be made 2.0 cm long with a tolerance of 4%. Set up an equation to solve for the shortest and longest bolt length. Show your original equation and the process used to find the shortest and longest bolt length.

Answer 1

The equations are:

`\text{shortest} = \text{length} - \frac{\text{tolerance}}{100}*\text{length}\\\text{shortest} = 2 - (4)/(100)*2 = 1.92\\\text{longest} = \text{length} + \frac{\text{tolerance}}{100}*\text{length}\\\text{longest} = 2 + (4)/(100)*2 = 2.08\\`

Explanation:

The ideal length of the bolt is 2.0 cm, since it has a tolerance of 4%, this means that length values between
`2 + (4)/(100)*2` and
`2 - (4)/(100)*2` are acceptable, because by those expressions the length of the bolt will be 4% higher or lower than it's original length. With this in mind let's find it's values:

`\text{shortest} = \text{length} - \frac{\text{tolerance}}{100}*\text{length}\\\text{shortest} = 2 - (4)/(100)*2 = 1.92\\\text{longest} = \text{length} + \frac{\text{tolerance}}{100}*\text{length}\\\text{longest} = 2 + (4)/(100)*2 = 2.08\\`