<p>There are 45 musicians in an orchestra, and all play two instruments. Of these musicians, 36 play the piano, and 22 play the violin. What is the maximum possible orchestra members who play both the piano and the violin?</p>
<p>The answer is 22, but i said 13. Please help me figure this out.</p>
<p>Well all play two instruments. That means that the 22 violin players play two instruments. All of these could play the piano as the other instrument, meaning that 22 is the maximum number. It’s more a word problem than a math problem, there’s not much math.</p>
<p>Yes, the answer is 22. Is there any particular reason why you answered 13?</p>
<p>A key element in the question is understanding that there are instruments in an orchestra beyond a piano and violin, lol</p>
<p>All kidding aside, that’s part of the trick of the question…</p>
<p>None of the above explanations are really making much sense (to me at least).</p>
<p>Correct me if I’m wrong but the formula setup should be:</p>
<p>total=(piano)+(violin)-(both)
45= 36+22-(b)
45=58-b
b=13</p>
<p>Something here is fishy…</p>
<p>The question did not state that the people playing the piano ONLY played the piano, and same for the violin. So, all 22 of the violin players could be a part of the 36 piano players as well.</p>
@JustinR I have come across the same problem with the same answer of 13 people. My reasoning is that since there are 45 musicians, the sum of those who play both piano and violin and those who don’t have to add up to 45. So if there were 13 violinists that did play both violin and piano, that would leave 9 that play violin alone. Along with the 23 pianists that play alone, that would leave 45 total musicians.
I realize that this post is 5 years old (time flies eh?) but I was just putting this out there because it’d be better than not doing so.
Thanks anyway!
@Deferno54 A better explanation is that the number of the “both” players equals anything above 45 when all is added. So, 67-45 = 22.