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The Venn diagram phrase issues on this lesson will present you use Venn diagrams with 2 circles to resolve issues involving counting.

## Venn diagram phrase issues with two circles

**Phrase drawback #1**

A survey was carried out in a neighborhood with 128 households. The survey revealed the next data.

- 106 of the households have a bank card
- 73 of the households try to repay a automotive mortgage
- 61 of the households have each a bank card and a automotive mortgage

**Reply the next questions:**

**1.** What number of households have solely a bank card?

**2.** What number of households have solely a automotive mortgage?

**3.** What number of households have neither a bank card nor a automotive mortgage?

**4.** What number of households shouldn’t have a bank card?

**5.** What number of households shouldn’t have a automotive mortgage?

**6.** What number of households have a bank card or a automotive mortgage?

- Let C be households with a bank card
- Let L be households with a automotive mortgage
- Let S be the full variety of households

The Venn diagram above can be utilized to reply all these questions.

**Recommendations on create the Venn diagram.**

All the time put first, within the center or within the intersection, the worth that’s in each units. For instance, since 61 households have each a bank card and a automotive mortgage, put 61 within the intersection earlier than you do anything.

In C solely, put 45 since 106 – 61 = 45

In L solely, put 12 since 73 – 61 = 12

Exterior C and L, put 10 since 128 – 61 – 45 – 12 = 10

**Resolution**

The expression, “solely a bank card” signifies that it is just in C. Any quantity in L can’t be included.

**1. **The variety of households with solely a bank card is 45. Don’t add 61 to 45 since 61 is in L.

**2. **The variety of households with solely a automotive mortgage is 12.

**3.** The variety of households with neither a bank card nor a automotive mortgage is 10. 10 is just not in C nor in L.

**4.** The quantity households with out a bank card is discovered by including every little thing that isn’t in C.

12 + 10 = 22

**5.** The quantity households with out a automotive mortgage is discovered by including every little thing that isn’t in L.

45 + 10 = 55

**6.** The variety of households with a bank card or a automotive mortgage is discovered by including something in C solely, in L solely and within the intersection of C and L?

45 + 61 + 12 = 118

**Phrase drawback #2**

A survey carried out in a college with 150 college students revealed the next data:

- 78 college students are enrolled in swimming class
- 85 college students are enrolled in basketball class
- 25 are enrolled in each swimming and basketball class

**Reply the next questions:**

**1.** What number of college students are enrolled solely in swimming class?

**2.** What number of college students are enrolled solely in basketball class?

**3.** What number of college students are neither enrolled in swimming class nor basketball class?

**4.** What number of college students are usually not enrolled in swimming class?

**5.** What number of college students are usually not enrolled in basketball class?

**6.** What number of college students are enrolled in swimming class or basketball class?

- Let S be college students enrolled in swimming class
- Let B be college students enrolled in basketball class
- Let E be the full variety of college students

Utilizing the identical method as in **drawback #1**, we now have the next Venn diagram

**1.** The variety of college students enrolled solely in swimming class is 53

**2. **The variety of college students enrolled solely in basketball class is 60

**3.** The variety of college students who’re neither enrolled in swimming class nor basketball class is 12

**4.** College students not enrolled in swimming class are enrolled in basketball class solely or are enrolled in neither of those two actions. In different phrases, every little thing that isn’t in S.

60 + 12 = 72

**5.** College students not enrolled in basketball class are enrolled in swimming class solely or are enrolled in neither of those two actions. In different phrases, every little thing that isn’t in B.

53 + 12 = 65

**6.** The variety of college students enrolled in swimming class or basketball class is discovered by including something in S solely, in B solely and within the intersection of S and B?

53 + 25 + 60 = 138

## A difficult Venn diagram phrase drawback with two circles

**Phrase drawback #3**

In a survey of 100 folks, 28 folks smoke, 65 folks drink, and 30 folks do neither. How many individuals do each?

**Resolution**

- Let Ok be the quantity of people that smoke
- Let D be the quantity of people that drink
- Let E be the full variety of folks
- Let x be the quantity of people that smoke and drink

If we make a Venn diagram, here’s what we now have to date.

We find yourself with the next equation to resolve for x.

(65 – x) + x + (28 – x) + 30 = 100

65 – x + x + 28 – x + 30 – 30 = 100 – 30

65 – x + x + 28 – x = 70

65 + 0 + 28 – x = 70

93 – x = 70

Since 93 – 23 = 70, x = 23

The quantity of people that do each is 23.

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