Mrs. Smith surprised her 30 students with cookies. She gave them a choice of chocolate chip, peanut butter and sugar cookies. 5 students had only a chocolate chip cookie, 3 had only a peanut butter cookie, and 2 had only a sugar cookie. 5 students had a chocolate chip cookie and a peanut butter cookie, 5 students had a sugar cookie and a peanut butter cookie, 6 had a chocolate chip and a sugar cookie, and 4 students had all three. How many students were vegans and chose not to have a cookie?
I only have 10 minutes to submit this! Please help me..
no experience with Venn diagrams?
The numbers are for disjoint sections of the diagram, so there's no overlap. They add up to 26, meaning that 4 students fit none of the categories.
No idea whether the choice to eschew the cookies (rather than chewing them) was because they were vegan.
FYI, running here for help at the last minute will likely make you miss your deadline, most of the time.
Mrs. Smith surprised her 30 students with cookies. She gave them a choice of chocolate chip, peanut butter and sugar cookies. 5 students had only a chocolate chip cookie, 3 had only a peanut butter cookie, and 2 had only a sugar cookie. 5 students had a chocolate chip cookie and a peanut butter cookie, 5 students had a sugar cookie and a peanut butter cookie, 6 had a chocolate chip and a sugar cookie, and 4 students had all three. How many students were vegans and chose not to have a cookie?
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Mrs. Smith surprised her 30 students with cookies. She gave them a choice of chocolate chip, peanut butter and sugar cookies. 5 students had only a chocolate chip cookie, 3 had only a peanut butter cookie, and 2 had only a sugar cookie. 5 students had a chocolate chip cookie and a peanut butter cookie, 5 students had a sugar cookie and a peanut butter cookie, 6 had a chocolate chip and a sugar cookie, and 4 students had all three. How many students were vegans and chose not to have a cookie?
To find out how many students were vegans and chose not to have a cookie, we need to count the number of students who are not mentioned in the given information.
Let's break it down step-by-step:
1. Total number of students: 30
2. Students with a chocolate chip cookie only: 5
Students with a peanut butter cookie only: 3
Students with a sugar cookie only: 2
3. Students with a chocolate chip cookie and a peanut butter cookie: 5
Students with a sugar cookie and a peanut butter cookie: 5
Students with a chocolate chip cookie and a sugar cookie: 6
4. Students who had all three types of cookies: 4
Now, let's calculate the number of students who are vegans and chose not to have a cookie.
We find the total number of students who had at least one type of cookie by adding the numbers in steps 2 and 3.
Total students with at least one cookie = (Students with a chocolate chip cookie only) + (Students with a peanut butter cookie only) + (Students with a sugar cookie only) + (Students with a chocolate chip cookie and a peanut butter cookie) + (Students with a sugar cookie and a peanut butter cookie) + (Students with a chocolate chip cookie and a sugar cookie) + (Students who had all three types of cookies)
= 5 + 3 + 2 + 5 + 5 + 6 + 4
= 30
Since the total number of students is 30, and all of them had at least one cookie, we can conclude that there were no students who were vegans and chose not to have a cookie.