A research based on 150 students relating to their favorite fruit revealed the
following: 90 students preferred Apples; 75 preferred Bananas; and 55 preferred Strawberries; 30 of them
preferred Bananas and Strawberries; 15 preferred Apples and Strawberries; 15 preferred Bananas only; 20 preferred Strawberries only.
2.1 Draw a Venn diagram to illustrate this information.
2.2 How many preferred bananas and apples but not strawberries?
2.3 How many preferred Bananas or apples but not strawberries?
2.4 What is the ratio of the number of students who preferred only Bananas to those who preferred both apples and strawberries?
2.5 What is the ratio of the number of students who preferred only Bananas to only Strawberries to only apples?
2.6 How many preferred apples only?
2.7 How many preferred all three fruits?
2.8 Which is the greater number: those who preferred both apples and strawberries, OR those who preferred both strawberries and bananas. By what percent is it greater?
2.9 In order to gain more insight on the student preferences, twenty one (21) students from another school were asked about their favorite fruits. Three of them did not like any of the three fruits. Six of them preferred both apples and strawberries. eight of them preferred both strawberries and bananas. Four of them preferred all three fruits. Only one student preferred strawberries only. Another student preferred bananas only.
(a) How many of the twenty one students preferred apples only? Give reasons
(b) From the total of one hundred and seventy one (171) students from both schools what is the number of students who do not like any of the three fruits?
do the math
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2.1 To draw a Venn diagram to illustrate this information, we need to first understand the relationships between the different preferences.
Let's label the regions of the Venn diagram as follows:
- A: Apples
- B: Bananas
- S: Strawberries
- AB: Apples and Bananas
- AS: Apples and Strawberries
- BS: Bananas and Strawberries
- ABS: All three fruits
The information given tells us:
- 90 students preferred Apples (A)
- 75 students preferred Bananas (B)
- 55 students preferred Strawberries (S)
- 30 students preferred Bananas and Strawberries (BS)
- 15 students preferred Apples and Strawberries (AS)
- 15 students preferred Bananas only (B)
- 20 students preferred Strawberries only (S)
Based on this information, we can now draw the Venn diagram. Here's a simple representation:
AS S
/ \
15 /___________\ 20
\ /
AB BS
\ /
_______
/ \
A /___________\ B
15 30
2.2 To find the number of students who preferred bananas and apples but not strawberries, we need to subtract the number of students who preferred all three fruits (ABS) from the number of students who preferred both apples and bananas (AB).
So, the number of students who preferred bananas and apples but not strawberries is 15 - 4 = 11.
2.3 To find the number of students who preferred Bananas or apples but not strawberries, we need to add the number of students who preferred bananas only (B) to the number of students who preferred apples only (A), and then subtract the number of students who preferred all three fruits (ABS).
So, the number of students who preferred Bananas or apples but not strawberries is (15 + 15) - 4 = 26.
2.4 The ratio of the number of students who preferred only Bananas (B) to those who preferred both apples and strawberries (AS) is given by B:AS.
In this case, the ratio is 15:15, which simplifies to 1:1.
2.5 The ratio of the number of students who preferred only Bananas (B) to only Strawberries (S) to only Apples (A) is given by B:S:A.
In this case, the ratio is 15:20:15, which simplifies to 3:4:3.
2.6 To find the number of students who preferred apples only (A), we need to subtract the number of students who preferred both apples and strawberries (AS) from the number of students who preferred apples (A).
So, the number of students who preferred apples only is 90 - 15 = 75.
2.7 To find the number of students who preferred all three fruits (ABS), we can directly read it from the Venn diagram.
From the diagram, we see that the number of students who preferred all three fruits is 4.
2.8 To determine whether the number of students who preferred both apples and strawberries (AS) or those who preferred both strawberries and bananas (BS) is greater, we can compare the respective numbers.
From the Venn diagram, we see that the number of students who preferred both apples and strawberries (AS) is 15, while the number of students who preferred both strawberries and bananas (BS) is 30.
To calculate the difference in percent, we can use the formula: (Difference / Larger Number) * 100.
In this case, the difference is 30 - 15 = 15.
The larger number is 30, so the percent difference is (15 / 30) * 100 = 50%.
Therefore, the number of students who preferred both strawberries and bananas is greater by 50%.
2.9 (a) To find the number of students who preferred apples only from the additional 21 students, we need to subtract the number of students who preferred both apples and strawberries (6) and the number of students who preferred all three fruits (4) from the total number of students who preferred apples (A), which is 90.
So, the number of students who preferred apples only is 90 - 6 - 4 = 80.
(b) To find the number of students who do not like any of the three fruits from the total of 171 students, we add the number of students from the first school who did not like any of the three fruits (0) to the number of students from the additional 21 students who did not like any of the three fruits (3).
Therefore, the total number of students who do not like any of the three fruits is 0 + 3 = 3.