Bunuel
A certain bakery baked a batch of 500 cookies one day. Of those, 320 contained nuts, 230 contained chocolate chips, and 85 contained neither nuts nor chocolate chips. What is the fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch?
A. 166
B. 275
C. 413
D. 438
E. 511
Thanks in advance for any reply !!
Please help me in understanding this question correctly!!
Since the question asks for "fewest possible cookies", shouldn't it be that we consider maximum overlap between 320 and 230 i.e. 230 rather 135 and then try to find the "fewest possible number of cookies with both chocolate chips and nuts that would need to be added to that batch so that cookies with both nuts and chocolate chips represented more than 3/5 of all the cookies in the batch"
Considering, 230 as the maximum overlap to find fewest possible .... 3/5 of all the cookies in the batch, as stated above in the solution by
Skywalker18. The equation would become as below:
(230+x)/(500+x)=6/10
x=175
why is this not correct ? or why is it wrong to consider 230 already having both nuts and choco chips rather than 135?
Thanks in advance.