Mrs. Benjamin baked some butter cookies and chocolate chip cookies in the ratio 7:3. After giving away 24 butter cookies, the ratio of butter cookies to chocolate chip cookies was 11:6. She then packed the rest of the cookies into bags of 4 without mixing them. How many bags of cookies of each type did she have?

We have 28 bags of butter cookies and 12 bags of chocolate chip cookies

Step-by-step explanation:

Let b be the number of butter cookies and c the number of chocolate chips.

Since we have them in the ratio 7:3, b/c = 7/3   (1)

Also, when Mrs Benjamin gives away 24 butter cookies, the ratio becomes 11:6. So, the remaining number of butter cookies are b - 24. So, the ratio of remaining butter cookies to chocolate chips is (b - 24)/c = 11/6   (2)

From (1) b = 7c/3 and from (2) 6(b - 24)  = 11c  ⇒  6b - 144 = 11c  (3)

Substituting b into (3), we have

6b - 144 = 11c

6(7c/3) - 144 = 11c

2 × 7c - 144 = 11c

14c - 144 = 11c

subtracting 11c from both sides, we have

14c - 11c - 144 = 11c - 11c

14c - 11c - 144 = 0

adding 144 to both sides, we have

14c - 11c -144 + 144 = 144

14c - 11c = 144

3c = 144

c = 144/3

c = 48

So, b = 7c/3 = 7(48)/3 = 7 × 16 = 112

Since each cookie is packed into bags of 4, we divide the number of each cookie by 4 to find the number of bags of cookies.

So, number of bags of butter cookies = b/4 = 112/4 = 28 bags of butter cookies

number of bags of chocolate chip cookies = c/4 = 48/4 = 12 bags of chocolate chip cookies

So, we have 28 bags of butter cookies and 12 bags of chocolate chip cookies

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step-by-step explanation:

geometry: triangles

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answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

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