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
<u>So, we have 28 bags of butter cookies and 12 bags of chocolate chip cookies</u>
