Question 1114654
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I can't draw the picture; but I can describe it....<br>
take all 3 (BCM): x  (what we are to find)
take BC only: 0  (all Chemistry students also take math)
take BM only: 9  (given)
take CM only: 50-x  (the 50 that take Chemistry and therefore math also, minus the x that take all 3)
take M only: 16  (given)
take C only: 0  (all Chemistry students take math also)
take B only: 64-x-9  {the total number of Biology students, minus those who take only BC, minus those who take only BM, minus those who take all 3)
take none: 5  (given)<br>
The total number of students is 105:<br>
{{{x+0+9+(50-x)+16+0+(64-x-9)+5 = 105}}}
{{{135-x = 105}}}
{{{x = 30}}}<br>
Answer: 30 students take all three courses.