By 11 am she had used up her whole supply of butter and switched to ginger snaps. When she took a break for lunch, she counted the cookies and noticed that she

Question

One day in December Grace decided to bake Christmas cookies to give to friends as gifts. She baked two types of cookies: ginger snaps and shortbread. She started with shortbread cookies. By 11 am she had used up her whole supply of butter and switched to ginger snaps. When she took a break for lunch, she counted the cookies and noticed that she already had four dozen ginger snaps, and that one quarter of the cookies baked so far were ginger snaps. After lunch, she continued baking ginger
snaps until three-quarters of the cookies were ginger snaps. In total, how many
dozen cookies did she bake that day?

Answer 1

Hello again.

 

Take this step by step.

At lunch break, Grace has 48 (4 dozen) ginger snap cookies, which is a quarter of the total at this time.

So, at lunch break, she has a total of 4*48 = 192 cookies, of which 144 (192-48) must be shortbread.

 

She keeps baking more ginger snaps until 3/4 of the new total are ginger snaps. Let's call n the number of additional cookies (all ginger snap) she baked since her lunch break. Then:

 

48+n = (3/4)*(192+n)

 

because the new number of ginger snaps is 48+n and the new total number of cookies is 192+n.

 

Now, just solve for n:

 

Multiply both sides of the equation by 4 to get:

 

192+4n = 3*(192+n) = 576+3n.

 

Therefore n = 576-192 = 384.

 

So the total number of cookies that Grace baked is:

 

T = 192+384 = 576.