Cookies

[N:Dure]

Cape Cod Cookies makes cookies of identical size from batches of cookie dough weighing 600 ounces. Cape Cod Cookies decides to modify the recipe by decreasing the weight of each cookie by 1 ounce. If Cape Cod Cookies discovers that it is now able to make 30 more cookies using the same batch of dough weighing 600 ounces, how much did each cookie originally weigh?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6


I got 5, is this correct?

[Tani]

Yes - try backsolving:

600 ounces divided by 5 ounces gives 120 cookies.

600 ounces divided by 4 ounces gives 150 cookies = or 30 more

[N:Dure]

Thanks Tani for the quick reply! can't believe I'm actually solving problems :'(

[Tani]

If you are uncomfortable working with variables, backsolving and picking numbers can make problems much easier to understand and solve. good luck!

[Jeff@TargetTestPrep]

Cape Cod Cookies makes cookies of identical size from batches of cookie dough weighing 600 ounces. Cape Cod Cookies decides to modify the recipe by decreasing the weight of each cookie by 1 ounce. If Cape Cod Cookies discovers that it is now able to make 30 more cookies using the same batch of dough weighing 600 ounces, how much did each cookie originally weigh?

(A) 2
(B) 3
(C) 4
(D) 5
(E) 6

We can let w = original weight of each cookie in ounces and c = the original number of cookies. Thus we have:

wc = 600

When the weight of each cookie is reduced by 1 ounce, the number of cookies is increased by 30, so we have:

(w - 1)(c + 30) = 600

Expanding the second equation we have:

wc + 30w - c - 30 = 600

Since wc = 600, we have:

600 + 30w - c - 30 = 600

30w - c - 30 = 0

Also since wc = 600, c = 600/w. So we have:

30w - 600/w - 30 = 0

Multiply the entire equation by w, we have:

30w^2 - 600 - 30w = 0

w^2 - w - 20 = 0

(w - 5)(w + 4) = 0

w = 5 or w = -4

Since w can't be negative, w = 5.

Answer: D