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:

$TotalCookies*\frac{1}{3}=CookiesBurned$

And the total cookies is given by:

$TotalCookies=CookiesBurned+CookiesUnburned$

Substituing:

$(CookiesBurned+CookiesUnburned)*\frac{1}{3}=CookiesBurned$

Replacing:

$(CookiesBurned+45)*\frac{1}{3}=CookiesBurned$

Solving for cookies Burned:

$\begin{gathered} \frac{CookiesBurned}{3}+\frac{45}{3}=CookiesBurned \\ 15=CookiesBurned-\frac{1}{3}CookiesBurned \\ 15=\frac{2}{3}CookiesBurned \\ CookiesBurned=15*\frac{3}{2}=\frac{45}{2} \end{gathered}$

Finally the percentage is given by:

$\frac{CookiesBurned}{TotalCookies}*100$

Replacing:

$\frac{\frac{45}{2}}{(\frac{45}{2}+45)}*100=\frac{1}{3}*100=33.3$

The percentage of Cookies were burned is 33.3%.