Counting Problem

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<p>If 15 of the trays contain a cup, then 10 do not contain a cup.</p>

<p>And if 21 trays contain plates, and 10 contain plates only, then 21-10= 11 trays contain both plates and cups.</p>

<p>Oh ok. But I don’t see why my method doesn’t work:</p>

<p>I made a Venn Diagram and set the cups = 15, the plates = 21, and the trays containing cups and plates = x. There are a total of 25 trays, so … </p>

<p>25 = 15 + 21 - 2x (x being the trays with both a cup and plate)</p>

<p>25 = 36 - 2x</p>

<p>-11 = -2x</p>

<p>x = non-integer (impossible).</p>

<p>Why 2x? It’s supposed to be x only.</p>

<p>Wow, I overcounted again :mad:.</p>

<p>Haha, it’s good that you’re making these mistakes in practice, meaning that you won’t make them again in the real thing. Keep working :)</p>

<p>A intersect B = A + B - (A U B)</p>

<p>This implies 11.</p>

<p>I just did there are 4 trays that don’t have plates and 10 trays that don’t have cups and subtracted 25-(4+10)=11.</p>