Question

A toy maker wants to re-create the Wright Brothers 1903 airplane. The actual plane was 21 feet long. The toy maker wants to use a scale model of 3 feet = 2 inches. How long will the replica plane be?

Answer 1

`x = 14ft`

Explanation:

Given

`Actual\ Length = 21ft`

Model:

`3\ ft = 2\ in`

Required

Determine the length of the replica

Represent the model as a ratio:

`Ratio = 3\ in:2\ ft`

Convert to fraction

`Ratio = (3\ in)/(2\ ft)`

Represent the actual lengths as a ratio

`Ratio = 21\ ft : x`

Where x is the length of the replica

Convert to fraction

`Ratio = (21\ in)/(x)`

Equate both ratios (because they are in proportion)

`(3\ in)/(2\ ft) = (21\ in)/(x)`

`(3)/(2\ ft) = (21)/(x)`

Cross Multiply:

`3 * x = 21 * 2\ ft`

`3x = 42\ ft`

Solve for x

`x = (42ft)/(3)`

`x = 14ft`

Hence, the length of the replica is 14ft