Question about Cookies

Question

2. A baker makes one batch of cookie dough, following his favorite cookie recipe. The dough will be divided evenly into some number n of cookies. The width w (in inches) of each cookie will depend on the number of cookies he intends to make.a.The width w of each cookie is either directly or inversely proportional to the square root of n.

a. Explain why this proportionality should be inverse instead of direct. b.Using this recipe, it is possible to make 48 cookies, each 2 inches wide. Using this clue, find a general formula for w in terms of n.

c.A visit to a first-grade class calls for 70 cookies. How large can each be?d.The baker’s son enjoys huge 6-inch-wide cookies. How many such monstrosities can be made with this recipe?

Answer 1

The more cookies, there is less room on the baking sheet. So the width must get smaller.

 

w = k/sqrt(n)

 

2 = k/sqrt(48)

 

2 * sqrt(48) = k

 

2 * sqrt(16*3) = k

 

2 * sqrt(16)*sqrt(3) = k

 

2*4*sqrt(3) = k

 

8*sqrt(3) = k

 

k = 8*sqrt(3) or "8 rad 3"

 

The function is W = 8*sqrt(3)/sqrt(n)

 

 

 

W = 8*sqrt(3)/sqrt(70)  or roughly 1.65 inches

 

6 = 8*sqrt(3)/n

 

n = 8*sqrt(3)/6 = (4/3)*sqrt(3) = 2.31, only 2 of them