Question

The diameter of the raw cookie is 2 1 2 inches. After baking the cookie, the diameter is 5 1 2 inches. By what factor does the cookie expand?

Answer 1

`Factor = 220 \%`

Explanation:

Given

`Initial = 2(1)/(2)`

`Final = 5(1)/(2)`

Required

Determine the factor of increment

First, we calculate the percentage increment

`\% Increment = (Final - Initial)/(Initial) * 100\%`

Substitute values for Final and Initial

`\% Increment = (5(1)/(2) - 2(1)/(2))/(2(1)/(2)) * 100\%`

Express fractions as decimals

`\% Increment = (5.5 - 2.5)/(2.5) * 100\%`

`\% Increment = (3)/(2.5) * 100\%`

`\% Increment = (3* 100)/(2.5) \%`

`\% Increment = (300)/(2.5) \%`

`\% Increment = 120 \%`

So, the factor of increment is:

`Factor = 100\% + Increment`

`Factor = 100\% + 120 \%`

`Factor = 220 \%`