A certain bakery baked a batch of 530 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? Choose one:
A) 166	B) 275	C) 413	D) 438	E) 533
Cookies which have both nuts and chocolate chips = 105   Let 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 = x   (105+x)/(530+x) = 6/10   =&gt;1050 + 10x = 3180 + 6x   =&gt; 4x = 2130   =&gt; x = 532.5   Therefore x = 533   Answer 533
<result>E</result>
A certain bakery baked a batch of 530 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?