Three set problem

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In a school of 120 students it was found out that 75 read English, 55 read science and 35 read biology. All the 120 students read at least one of three subject and 49 read exactly two subjects. How many students read all the three subjects?



I have spent all day but I couldn't solve it help me please!




elementary-set-theory




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  • I have spent all day but I couldn't solve it help me please!
    – user578668
    Jul 22 at 6:17










  • Have you drawn a Venn diagram?
    – Lord Shark the Unknown
    Jul 22 at 6:22










  • I have but I couldn't use it to solve it
    – user578668
    Jul 22 at 6:23










  • Help me with the workings
    – user578668
    Jul 22 at 6:30














up vote
0
down vote

favorite












In a school of 120 students it was found out that 75 read English, 55 read science and 35 read biology. All the 120 students read at least one of three subject and 49 read exactly two subjects. How many students read all the three subjects?



I have spent all day but I couldn't solve it help me please!




elementary-set-theory




share|cite|improve this question





















  • I have spent all day but I couldn't solve it help me please!
    – user578668
    Jul 22 at 6:17










  • Have you drawn a Venn diagram?
    – Lord Shark the Unknown
    Jul 22 at 6:22










  • I have but I couldn't use it to solve it
    – user578668
    Jul 22 at 6:23










  • Help me with the workings
    – user578668
    Jul 22 at 6:30












up vote
0
down vote

favorite









up vote
0
down vote

favorite











In a school of 120 students it was found out that 75 read English, 55 read science and 35 read biology. All the 120 students read at least one of three subject and 49 read exactly two subjects. How many students read all the three subjects?



I have spent all day but I couldn't solve it help me please!




elementary-set-theory




share|cite|improve this question













In a school of 120 students it was found out that 75 read English, 55 read science and 35 read biology. All the 120 students read at least one of three subject and 49 read exactly two subjects. How many students read all the three subjects?



I have spent all day but I couldn't solve it help me please!





elementary-set-theory





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Jul 22 at 6:20









Parcly Taxel

33.6k136588




33.6k136588









asked Jul 22 at 6:15









user578668

11




11











  • I have spent all day but I couldn't solve it help me please!
    – user578668
    Jul 22 at 6:17










  • Have you drawn a Venn diagram?
    – Lord Shark the Unknown
    Jul 22 at 6:22










  • I have but I couldn't use it to solve it
    – user578668
    Jul 22 at 6:23










  • Help me with the workings
    – user578668
    Jul 22 at 6:30
















  • I have spent all day but I couldn't solve it help me please!
    – user578668
    Jul 22 at 6:17










  • Have you drawn a Venn diagram?
    – Lord Shark the Unknown
    Jul 22 at 6:22










  • I have but I couldn't use it to solve it
    – user578668
    Jul 22 at 6:23










  • Help me with the workings
    – user578668
    Jul 22 at 6:30















I have spent all day but I couldn't solve it help me please!
– user578668
Jul 22 at 6:17




I have spent all day but I couldn't solve it help me please!
– user578668
Jul 22 at 6:17












Have you drawn a Venn diagram?
– Lord Shark the Unknown
Jul 22 at 6:22




Have you drawn a Venn diagram?
– Lord Shark the Unknown
Jul 22 at 6:22












I have but I couldn't use it to solve it
– user578668
Jul 22 at 6:23




I have but I couldn't use it to solve it
– user578668
Jul 22 at 6:23












Help me with the workings
– user578668
Jul 22 at 6:30




Help me with the workings
– user578668
Jul 22 at 6:30










1 Answer
1






active

oldest

votes

















up vote
0
down vote













By the Principle of Inclusion Exclusion, we must add up the number of students reading English, the number of students reading Science, and the number of students reading Biology. Then we must subtract this sum from the number of people reading English and Science, the number of people reading Science and Biology, and the number of students reading Biology and English. Finally, we must add back the number of students reading all three of the subjects; this calculates the number of students in the school. Let $x$ be the number of students reading all three of the subjects. We now have the equation



$75+55+35-49+x=120$



Solving for $x$ yields $boxed4$ as the number of students reading all three of the subjects.






share|cite|improve this answer





















  • Can you break it down for me
    – user578668
    Jul 22 at 6:36










  • Yes; so in the Venn Diagram, we have three intersecting circles right? We already know the number of students described in the diagram is $120.$ We want to set up an expression to help us find the middle part where all three circles intersect; call that $x.$ Now, we start by adding the sizes of each individual circle; don't worry about intersections. So we have $75+55+35.$ However, now we are counting the three intersection regions of two circles twice; we only want it once, so we subtract the collective size of those regions. The problem says this size is $49,$ so we subtract that.
    – Flynn Rixona
    Jul 22 at 6:43










  • Now, notice that we counted the region where all three circles are intersecting three times from just looking at the individual circles, but then subtracted this region three times when looking at the intersections of two circles. So, we want to add this part back in. Using all of this, we can set up the equation in my solution to solve for $x.$
    – Flynn Rixona
    Jul 22 at 6:46










  • Thanks you very much
    – user578668
    Jul 22 at 6:50










  • But how did you count for those who read exactly two subject (49)
    – user578668
    Jul 22 at 6:53










Your Answer




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1 Answer
1






active

oldest

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1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
0
down vote













By the Principle of Inclusion Exclusion, we must add up the number of students reading English, the number of students reading Science, and the number of students reading Biology. Then we must subtract this sum from the number of people reading English and Science, the number of people reading Science and Biology, and the number of students reading Biology and English. Finally, we must add back the number of students reading all three of the subjects; this calculates the number of students in the school. Let $x$ be the number of students reading all three of the subjects. We now have the equation



$75+55+35-49+x=120$



Solving for $x$ yields $boxed4$ as the number of students reading all three of the subjects.






share|cite|improve this answer





















  • Can you break it down for me
    – user578668
    Jul 22 at 6:36










  • Yes; so in the Venn Diagram, we have three intersecting circles right? We already know the number of students described in the diagram is $120.$ We want to set up an expression to help us find the middle part where all three circles intersect; call that $x.$ Now, we start by adding the sizes of each individual circle; don't worry about intersections. So we have $75+55+35.$ However, now we are counting the three intersection regions of two circles twice; we only want it once, so we subtract the collective size of those regions. The problem says this size is $49,$ so we subtract that.
    – Flynn Rixona
    Jul 22 at 6:43










  • Now, notice that we counted the region where all three circles are intersecting three times from just looking at the individual circles, but then subtracted this region three times when looking at the intersections of two circles. So, we want to add this part back in. Using all of this, we can set up the equation in my solution to solve for $x.$
    – Flynn Rixona
    Jul 22 at 6:46










  • Thanks you very much
    – user578668
    Jul 22 at 6:50










  • But how did you count for those who read exactly two subject (49)
    – user578668
    Jul 22 at 6:53














up vote
0
down vote













By the Principle of Inclusion Exclusion, we must add up the number of students reading English, the number of students reading Science, and the number of students reading Biology. Then we must subtract this sum from the number of people reading English and Science, the number of people reading Science and Biology, and the number of students reading Biology and English. Finally, we must add back the number of students reading all three of the subjects; this calculates the number of students in the school. Let $x$ be the number of students reading all three of the subjects. We now have the equation



$75+55+35-49+x=120$



Solving for $x$ yields $boxed4$ as the number of students reading all three of the subjects.






share|cite|improve this answer





















  • Can you break it down for me
    – user578668
    Jul 22 at 6:36










  • Yes; so in the Venn Diagram, we have three intersecting circles right? We already know the number of students described in the diagram is $120.$ We want to set up an expression to help us find the middle part where all three circles intersect; call that $x.$ Now, we start by adding the sizes of each individual circle; don't worry about intersections. So we have $75+55+35.$ However, now we are counting the three intersection regions of two circles twice; we only want it once, so we subtract the collective size of those regions. The problem says this size is $49,$ so we subtract that.
    – Flynn Rixona
    Jul 22 at 6:43










  • Now, notice that we counted the region where all three circles are intersecting three times from just looking at the individual circles, but then subtracted this region three times when looking at the intersections of two circles. So, we want to add this part back in. Using all of this, we can set up the equation in my solution to solve for $x.$
    – Flynn Rixona
    Jul 22 at 6:46










  • Thanks you very much
    – user578668
    Jul 22 at 6:50










  • But how did you count for those who read exactly two subject (49)
    – user578668
    Jul 22 at 6:53












up vote
0
down vote










up vote
0
down vote









By the Principle of Inclusion Exclusion, we must add up the number of students reading English, the number of students reading Science, and the number of students reading Biology. Then we must subtract this sum from the number of people reading English and Science, the number of people reading Science and Biology, and the number of students reading Biology and English. Finally, we must add back the number of students reading all three of the subjects; this calculates the number of students in the school. Let $x$ be the number of students reading all three of the subjects. We now have the equation



$75+55+35-49+x=120$



Solving for $x$ yields $boxed4$ as the number of students reading all three of the subjects.






share|cite|improve this answer













By the Principle of Inclusion Exclusion, we must add up the number of students reading English, the number of students reading Science, and the number of students reading Biology. Then we must subtract this sum from the number of people reading English and Science, the number of people reading Science and Biology, and the number of students reading Biology and English. Finally, we must add back the number of students reading all three of the subjects; this calculates the number of students in the school. Let $x$ be the number of students reading all three of the subjects. We now have the equation



$75+55+35-49+x=120$



Solving for $x$ yields $boxed4$ as the number of students reading all three of the subjects.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Jul 22 at 6:33









Flynn Rixona

1567




1567











  • Can you break it down for me
    – user578668
    Jul 22 at 6:36










  • Yes; so in the Venn Diagram, we have three intersecting circles right? We already know the number of students described in the diagram is $120.$ We want to set up an expression to help us find the middle part where all three circles intersect; call that $x.$ Now, we start by adding the sizes of each individual circle; don't worry about intersections. So we have $75+55+35.$ However, now we are counting the three intersection regions of two circles twice; we only want it once, so we subtract the collective size of those regions. The problem says this size is $49,$ so we subtract that.
    – Flynn Rixona
    Jul 22 at 6:43










  • Now, notice that we counted the region where all three circles are intersecting three times from just looking at the individual circles, but then subtracted this region three times when looking at the intersections of two circles. So, we want to add this part back in. Using all of this, we can set up the equation in my solution to solve for $x.$
    – Flynn Rixona
    Jul 22 at 6:46










  • Thanks you very much
    – user578668
    Jul 22 at 6:50










  • But how did you count for those who read exactly two subject (49)
    – user578668
    Jul 22 at 6:53
















  • Can you break it down for me
    – user578668
    Jul 22 at 6:36










  • Yes; so in the Venn Diagram, we have three intersecting circles right? We already know the number of students described in the diagram is $120.$ We want to set up an expression to help us find the middle part where all three circles intersect; call that $x.$ Now, we start by adding the sizes of each individual circle; don't worry about intersections. So we have $75+55+35.$ However, now we are counting the three intersection regions of two circles twice; we only want it once, so we subtract the collective size of those regions. The problem says this size is $49,$ so we subtract that.
    – Flynn Rixona
    Jul 22 at 6:43










  • Now, notice that we counted the region where all three circles are intersecting three times from just looking at the individual circles, but then subtracted this region three times when looking at the intersections of two circles. So, we want to add this part back in. Using all of this, we can set up the equation in my solution to solve for $x.$
    – Flynn Rixona
    Jul 22 at 6:46










  • Thanks you very much
    – user578668
    Jul 22 at 6:50










  • But how did you count for those who read exactly two subject (49)
    – user578668
    Jul 22 at 6:53















Can you break it down for me
– user578668
Jul 22 at 6:36




Can you break it down for me
– user578668
Jul 22 at 6:36












Yes; so in the Venn Diagram, we have three intersecting circles right? We already know the number of students described in the diagram is $120.$ We want to set up an expression to help us find the middle part where all three circles intersect; call that $x.$ Now, we start by adding the sizes of each individual circle; don't worry about intersections. So we have $75+55+35.$ However, now we are counting the three intersection regions of two circles twice; we only want it once, so we subtract the collective size of those regions. The problem says this size is $49,$ so we subtract that.
– Flynn Rixona
Jul 22 at 6:43




Yes; so in the Venn Diagram, we have three intersecting circles right? We already know the number of students described in the diagram is $120.$ We want to set up an expression to help us find the middle part where all three circles intersect; call that $x.$ Now, we start by adding the sizes of each individual circle; don't worry about intersections. So we have $75+55+35.$ However, now we are counting the three intersection regions of two circles twice; we only want it once, so we subtract the collective size of those regions. The problem says this size is $49,$ so we subtract that.
– Flynn Rixona
Jul 22 at 6:43












Now, notice that we counted the region where all three circles are intersecting three times from just looking at the individual circles, but then subtracted this region three times when looking at the intersections of two circles. So, we want to add this part back in. Using all of this, we can set up the equation in my solution to solve for $x.$
– Flynn Rixona
Jul 22 at 6:46




Now, notice that we counted the region where all three circles are intersecting three times from just looking at the individual circles, but then subtracted this region three times when looking at the intersections of two circles. So, we want to add this part back in. Using all of this, we can set up the equation in my solution to solve for $x.$
– Flynn Rixona
Jul 22 at 6:46












Thanks you very much
– user578668
Jul 22 at 6:50




Thanks you very much
– user578668
Jul 22 at 6:50












But how did you count for those who read exactly two subject (49)
– user578668
Jul 22 at 6:53




But how did you count for those who read exactly two subject (49)
– user578668
Jul 22 at 6:53












 

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