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

## Venn diagram phrase issues with two circles

**Phrase downside #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 are attempting 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 whole variety of households

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

**Tips about how you can 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 the rest.

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

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

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

**Answer**

The expression, “solely a bank card” implies 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 isn’t in C nor in L.

**4.** The quantity households and not using a bank card is discovered by including the whole lot that’s not in C.

12 + 10 = 22

**5.** The quantity households and not using a automotive mortgage is discovered by including the whole lot that’s not 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 downside #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 will not be enrolled in swimming class?

**5.** What number of college students will not be 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 whole variety of college students

Utilizing the identical approach as in **downside #1**, now we 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, the whole lot that’s not 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, the whole lot that’s not 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 tough Venn diagram phrase downside with two circles

**Phrase downside #3**

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

**Answer**

- Let Okay be the quantity of people that smoke
- Let D be the quantity of people that drink
- Let E be the whole variety of individuals
- Let x be the quantity of people that smoke and drink

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

We find yourself with the next equation to unravel 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.