<p>There are 25 trays ona table in the cafe. each tray contains a cup only, plate only, or both
if 15 contain cups and 21 contain plates
how many contain both ?</p>
<p>Answer is 11... I forget the trick/reasoning behind this. It also applies to when you know how many contain both and need to figure out how many the specific type contains. there was a thread on this sorta problem a LONG time ago and i can't find it....so if you know what im talking bout, link it.</p>
<p>this is essentially a sets question
just remember the formula
n(A U B) = n(A) + n(B) - n(A /\ B)
where U means union
and /\ means intersection
here n(A U B) is 25
n(A) is 21
n(B) is 15
so n(A/\B) turns out 11</p>
<p>any other answers?</p>
<p>21+15-25=11
I don’t think you need a formula, use your imagination 
( or venn diagram)</p>
<p>Mathsfreak has the right answer, but may be psyching you out with the set notation.</p>
<p>All he is saying is essentially: You have 15 cups and 21 plates. That adds up to 36 things. (You can say that there are 36 elements in the union of the two sets if you like saying that kind of thing.) But you have only 25 trays. So 36 - 25 = 11 more things than trays. So you are going to have to put those 11 items onto trays that already have an item. That’s how you know that 11 trays have both cup and plate.</p>
<p>Right but what if i knew that i had 11 of both and knew one of the other values, how would i solve it? or is it the same idea. add the two specific quantities together and subtract by the total amount? to find the other specific? like if i was given that i had 11 in common, and like 21 plates. how do i find how many cups?</p>
<p>I think that you need the amount of trays ( 25 ) in addition to 11 and 21 to find out how many cups. And I also think that after drawing a venn diagram, you will find the answer ( to all questions of this kind) easily</p>
<p>can someone give me an example of another type of “venn diagram” question and i’ll figure out the answer?</p>
<p>Here are a few, be sure to show how you solve them.</p>
<ol>
<li><p>There are 18 boys in the class: 6 play football, 5 play baseball, and 3 play on both teams. How many boys are NOT on either team?</p></li>
<li><p>Of the 25 students who play in the band, 12 play the drums, 7 play the trumpet, and 11 play neither the drums nor the trumpet. How many students play BOTH drums and trumpet?</p></li>
<li><p>In a class of 32 students, 28 passed the English test, 26 passed the History exam, and 24 passed both. How many students did not pass either English or History?</p></li>
<li><p>Club M has 11 members and Club R has 18. If a total of 24 people belong to the two clubs, how many people belong to both clubs?</p></li>
<li><p>A car dealer has 1,200 cars in stock of which 900 have air conditioners and 800 have CD players. If 80 of the cars have neither air conditioners nor CD players, how many cars on the lot must have BOTH air conditioners and CD players?</p></li>
</ol>