For Billy’s birthday party his mother has baked 80 cookies. 40 cookies contain vanilla and 45 contains nuts, and 15 contain both. One of Billy’s friends, Jim, is allergic to both nuts and vanilla, but he loves cookies! What is the largest number of cookies that Jim can eat on Billy’s birthday? (Note that it is fine for Jim to smell nuts and vanilla as long as he is not eating anything that contains them.)

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RenatoMattice RenatoMattice · Answer 1 · 2019-05-31T07:45:55+02:00

Answer: The maximum number of cookies eaten by Jim is 10.

Step-by-step explanation:

Since we have given that

Total number of cookies n(U) = 80

Number of cookies containing vanilla n(V) = 40

Number of cookies containing nuts n(N) = 45

Number of cookies containing both n(V∩N) = 15

So, we get that

[tex]n(V\cup N)=n(V)+n(N)-n(V\cap N)\\\\n(V\cup N)=40+45-15\\\\n(V\cup N)=85-15\\\\n(V\cup N)=70[/tex]

Since Jim is allergic to both nuts and vanilla, but he loves cookies.

So, number of cookies eaten by Jim which is neither nuts nor vanilla.

[tex]n(V\cup N)'=n(U)-n(V\cup N)\\\\n(V\cup N)'=80-70\\\\n(V\cup N)'=10[/tex]

Hence, the maximum number of cookies eaten by Jim is 10.

abiolataiwo2015 abiolataiwo2015 · Answer 2 · 2022-04-25T18:14:37+02:00

If his mother has baked 80 cookies. The largest number of cookies that Jim can eat on Billy’s birthday is 10 cookies.

First step

Number of nuts = 45 - 15

Number of nut = 30

Second step

Number of nuts and vanilla = 30 + 40

Number of nuts and vanilla = 70

Third step

Number of cookies= 80 - 70

Number of cookies= 10 cookies

Therefore the largest number of cookies that Jim can eat on Billy’s birthday is 10 cookies.

Learn more about Number of cookies here:https://brainly.com/question/3830204