A certain bakery baked a batch of 550 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?  Answers: A) 166 B) 275 C) 413 D) 438 E) 613
Cookies which have both nuts and chocolate chips = 85   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   (85+x)/(550+x) = 6/10   =&gt;850 + 10x = 3300 + 6x   =&gt; 4x = 2450   =&gt; x = 612.5   Therefore x = 613   Answer 613
<result>E</result>
A certain bakery baked a batch of 550 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?