Question

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?

Answer 1

Answer:

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