In a military camp,50 officers had a choice of beans,24 plantain and 18 rice. Also 3 chose beans only, 9 plantain only,2 rice only and 5 chose all three kinds of food.a, illustrate the information on a Venn diagram.
B.use the Venn diagram to find the number of Officers who chose.
i.plantain and beans only.
ii.exactly two kinds of food.
iii.none of the three kinds of food .
Filled in the given information on a Venn diagram, and was left with these
unknows:
the number for Beans and Plantain, but not rice
the number for Beans and Rice, but not Plantain
then number for Plantain and Rice but not Beans
I labeled these a, b, and c respectively, giving me these equations:
a+b+8 = 50 ---> a+b = 42 **
a+c+14 = 24 ---> a+c = 10 ***
b+c+7 = 18 ---> b+c = 11 ****
subtract *** from **
b - c = 26
add this to ****
2b = 44
b = 22 , then a = 20 and c = -10 <---- this makes no sens
Either there is a flaw in the data given, or else I did not interpret the
question correctly.
e.g.
did you mean: "In a military camp of 50 officers..." ?
then you should not have had that comma.
Look carefully at the wording.
Hamidu, there are no automatic answers here. Learn to post questions and then have patience until a tutor helps you.
To illustrate the information on a Venn diagram, you will need three overlapping circles representing the three kinds of food: beans, plantain, and rice. Let's label these circles as B (for beans), P (for plantain), and R (for rice).
Using the given information, we can fill in the overlapping regions of the Venn diagram:
1. We know that 3 officers chose beans only, so we place the number 3 in the region labeled B.
2. Similarly, 9 officers chose plantain only, so we place the number 9 in the region labeled P.
3. 2 officers chose rice only, so we place the number 2 in the region labeled R.
4. Finally, 5 officers chose all three kinds of food, so we place the number 5 in the overlapping region of B, P, and R.
Now, let's answer the questions using the Venn diagram:
A. To find the number of officers who chose plantain and beans only (i), we look at the overlap of regions B and P (excluding the overlap with R). From the diagram, it appears that there are no numbers in this region, indicating that no officers chose plantain and beans only.
B. To find the number of officers who chose exactly two kinds of food (ii), we look at the overlapping regions B and P, B and R, and P and R (excluding the overlap with all three). From the diagram, we can see that there are 3 officers who chose exactly two kinds of food.
C. To find the number of officers who chose none of the three kinds of food (iii), we look outside of all the regions of the Venn diagram, which is the portion not covered by any of the circles. From the diagram, it appears that there are no numbers in this region, indicating that no officers chose none of the three kinds of food.