Four companies A, B, C, and D produce butter and chocolate cookies. The total cookies produced by these companies are distributed as follows: A - 20%, B - N + 5%, C - N%, and D - N - 20% of the total production. The distribution of chocolate cookies among these companies is: A - 10%, B - M%, C - 40%, and D - 20% of the total chocolate cookies produced.

Given that the total number of butter cookies produced by companies A and B are 110 and 30 respectively, find the ratio of the total butter cookies produced by all four companies to the total chocolate cookies produced by all four companies.

Question

Four companies A, B, C, and D produce butter and chocolate cookies. The total cookies produced by these companies are distributed as follows: A - 20%, B - N + 5%, C - N%, and D - N - 20% of the total production. The distribution of chocolate cookies among these companies is: A - 10%, B - M%, C - 40%, and D - 20% of the total chocolate cookies produced.

Given that the total number of butter cookies produced by companies A and B are 110 and 30 respectively, find the ratio of the total butter cookies produced by all four companies to the total chocolate cookies produced by all four companies.

Accepted Answer

**Solution:**

1. Let the total number of cookies produced by all companies be 100 units for simplicity.

2. According to the data, the total butter cookies produced by all companies is the difference between total cookies and total chocolate cookies.

3. From the problem, the total butter cookies produced by A and B are 110 and 30 respectively.

4. Using the percentages, the total butter cookies produced by all companies can be calculated as:
   - Butter cookies = Total cookies - Chocolate cookies

5. Given the values, the ratio of total butter cookies to total chocolate cookies is:

$$	ext{Butter cookies} : 	ext{Chocolate cookies} = (100 	imes 10 - 100 	imes 6) : 100 	imes 6 = 400 : 600 = 2 : 3$$

**Answer:** 2 : 3

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