Mrs. Molasses prepared a variety of cookies. 3/5 of the cookies were peanut butter and 1/3 of the remaining cookies were gingerbread. There were 8 chocolate chip cookies. How many cookies did Mrs. Molasses prepare altogether?
Plz anyone??!
To find the total number of cookies, we need to find the fraction of cookies that were peanut butter and gingerbread, and then determine the total number of remaining cookies.
Let's start by finding the fraction of cookies that were peanut butter. We are given that 3/5 of the cookies were peanut butter. So, we can represent this as an equation:
3/5 * Total Cookies = Number of Peanut Butter Cookies
Next, we need to find the fraction of the remaining cookies that were gingerbread. We are given that 1/3 of the remaining cookies were gingerbread. Since the peanut butter cookies were already accounted for, the remaining cookies are the ones that were not peanut butter cookies. So, we can represent this as an equation:
(1 - Number of Peanut Butter Cookies/Total Cookies) * Total Cookies = Number of Gingerbread Cookies
Now, we know that there were 8 chocolate chip cookies. Since these cookies are neither peanut butter nor gingerbread, they make up the remaining fraction of cookies. So, we can represent this as an equation:
(Number of Chocolate Chip Cookies/Total Cookies) * Total Cookies = 8
To find the total number of cookies, we need to solve these equations simultaneously:
3/5 * Total Cookies = Number of Peanut Butter Cookies
(1 - Number of Peanut Butter Cookies/Total Cookies) * Total Cookies = Number of Gingerbread Cookies
(Number of Chocolate Chip Cookies/Total Cookies) * Total Cookies = 8
To make this calculation simpler, let's assume the total number of cookies is a variable x.
3/5 * x = Number of Peanut Butter Cookies ...(1)
(1 - Number of Peanut Butter Cookies/x) * x = Number of Gingerbread Cookies ...(2)
(Number of Chocolate Chip Cookies/x) * x = 8 ...(3)
From equation (1), we can solve for the number of peanut butter cookies:
Number of Peanut Butter Cookies = (3/5) * x
Substituting this value in equation (2), we can solve for the number of gingerbread cookies:
(1 - (3/5) * x/x) * x = Number of Gingerbread Cookies
(2/5) * x = Number of Gingerbread Cookies
Substituting the given value of 8 in equation (3), we can solve for x:
(Number of Chocolate Chip Cookies/x) * x = 8
Number of Chocolate Chip Cookies = 8
Since the number of chocolate chip cookies is given as 8, we can substitute this value in equation (3):
(8/x) * x = 8
8 = 8
This equation is true regardless of the value of x, which means x can be any positive number.
Therefore, we cannot determine the exact total number of cookies prepared by Mrs. Molasses based on the given information.
3/5 pb, leaving 2/5
1/3 * 2/5 = 2/15 gb
2/5 + 2/15 = 8/15
so, 7/15 were cc.
7/15 x = 8