Question

While making cookies willam accidentally over-baked and burned many of the cookies. His burned-to-unburned ratio was 1 to 3. He made 45 unburned cookies. What percent of the total cookies were burned

Answer 1

The ratio between burned-to-unburned is: 1/3.

William made 45 unburned cookies.

Percentage of cookies burned:

`TotalCookies*(1)/(3)=CookiesBurned`

And the total cookies is given by:

`TotalCookies=CookiesBurned+CookiesUnburned`

Substituing:

`(CookiesBurned+CookiesUnburned)*(1)/(3)=CookiesBurned`

Replacing:

`(CookiesBurned+45)*(1)/(3)=CookiesBurned`

Solving for cookies Burned:

`\begin{gathered} (CookiesBurned)/(3)+(45)/(3)=CookiesBurned \\ 15=CookiesBurned-(1)/(3)CookiesBurned \\ 15=(2)/(3)CookiesBurned \\ CookiesBurned=15*(3)/(2)=(45)/(2) \end{gathered}`

Finally the percentage is given by:

`(CookiesBurned)/(TotalCookies)*100`

Replacing:

`((45)/(2))/(((45)/(2)+45))*100=(1)/(3)*100=33.3`

The percentage of Cookies were burned is 33.3%.